In Dating, The First Cut is the Deepest
(N.B. All advice is personal and results will always vary; you may need to hear the exact opposite of what I have to say here. Maybe just keep it in your bag of tricks as you date in whatever way you see fit.)
From my ivory tower of being happily married (for all of four months), I can readily judge the rest of the world's methods of finding stable relationships, and find them wanting.
How do people typically find a partner?
If stories are to be believed, the standard method used to be going out; picking up guys/girls at a bar was real. So, you go out on Saturday night, see attractive people from across the bar, and try to talk to them. One downside seems to be the possibility of misunderstandings--some people really are just at the bar to hang out with their friends, not to be hit on!--and this can easily cross over into coercion (persuasion?) in the presence of inhibition-inhibiting alcohol. But also, there are only so many people out at a bar on Saturday night; your options are limited by interest, but also by bar capacity. Of course, it doesn't have to literally be a bar; maybe you can meet people at a bowling alley or a library or some other place that definitely still exists.
Modern people use modern technology to solve their problems, which in this case means dating apps (e.g. OK Cupid, Tinder, or Hinge). The basic strategy solves the numbers problem by showing people thousands of options, as many singles as there are in a given radius satisfying basic constraints, giving you have as many opportunities as you might want, in principle. But in practice, the bottleneck tends to be (on average) that men send a lot of messages that don't get answers, and women receive more messages than they can reasonably answer (including many creepy / offensive ones). So, like in the wild*, women are selectors and hold a large amount of sway in who succeeds in the mating world, but face serious dangers along the way.
I have tended to operate by a third strategy: date your friends. These are people with whom you know you share things in common and with whom you enjoy spending time. Not all of your friends would make a good partner for you, since almost nobody would, but if you date a friend, then before taking that first romantic step you have strongly filtered the population for a certain kind of compatibility.
The conventional wisdom is that you shouldn't date your friends. Often the stated reason is that you don't want to ruin the friendship if the romance gets awkward; in the worst case, one or both of you ends up resenting the other and the friendship falls apart with the relationship. To mitigate this, you might approach a friendship-->relationship transition with special care, pledging to be very open about the situation with the other person. Even so, I accept that this is a risk and it's bad when it happens. If you instead date only strangers, you can easily break all ties when you break up; it's cleaner.
This fact notwithstanding, I think it's probably to our detriment that we tend to have two separate boxes in our heads--"friends" and "potential partners"--and so people should more often consider dating their friends.
Here are three reasons why I advocate dating friends over the other methods:
1. You select for people whose company you enjoy.
You need to filter the pool of potential mates, and particular methods select for particular traits. Roughly speaking, going out seems to primarily select for attractiveness (that's generally all you have to go on before you talk to someone), but also maybe extraversion (they're out at a bar) and openness (they actually talk to strangers). Dating apps also select for attractiveness (e.g. "swipe right", for evidence see also this study if you can (sorry, paywall)), and probably some kind of creativity or boldness (to get replies to your first message requires you to really stand out from the crowd). On the other hand, dating your friends selects for whatever you select for in finding friends; in that sense, it's the most personalized of the three strategies.
Depending on what you're going for, each of these might be good filters for what you want. For people who are just looking for a hookup, in particular, the first two strategies may select more for people who are like-minded along that axis. There's nothing wrong with this goal if that's what you want; go and get your freak on if that's what you're after! But if your goal is to form a long-term relationship, it's not clear that selecting for attractiveness or extraversion should be expected to work. Yes, it's very good to have a partner who is attractive to you, but given a choice I would rather date someone I love spending time with than someone I find especially attractive. If you're going to sort your options by cutting on some quality of the candidates (and you are!), I recommend personality over looks.
Furthermore, note that...
2. Attractiveness is not fixed; it varies with personal connection and context.
Long before I met my wife, I dated someone for a while in grad school. She was a friend of my best friend's girlfriend that sort of found herself hanging out with all of us in a group. And while she had all the markers of traditional attractiveness, I found myself totally uninterested. She actually didn't look attractive to me physically. Why? Because I saw how she conducted herself. Her lifestyle choices made her difficult to trust, led her to flake out of plans and agreements between friends, and frequently got her into bad situations that her friends had to bail her out of. I didn't judge her on a personal level for any of this; she and I became friends in the midst of all this. But something about the situation covered her physical beauty, at least in my eyes, with a veneer of disinterest.
Over time, I discovered that, deep down, she was a sweet girl who was wrapped up in bad stuff but on a positive trajectory. As I got to know her, she literally became more attractive to me physically. I noticed her eyes, her warmth. Eventually we dated off-and-on, and while we agreed to go our separate ways, we are still good friends today.
I think this scales to some extent. The mental and the physical do not separate cleanly; I can show you a picture of a beautiful actress, and you might agree with that description, until I tell you that she got fired for some old racist tweets (if you're worried about that sort of thing). Or didn't you think Kevin Spacey was an attractive man, until you found out he was probably a sexual abuser? These are extreme cases, but they illustrate the point.
I admit, this effect likely only goes so far; there's good evidence that objective measures of traditional attractiveness--symmetry and proportionality, for example--are good predictors for who will get a job or receive more votes in an election, independently of context. But just because someone doesn't tickle your fancy at first sight, they may grow on you over time. And friendships have the advantage of time, as well.
3. The first selection is automatic, because you'll be trying to make friends anyway.
Dating is hard. At least, I felt like it was. All that time on dating apps, all those hopes and failures and missed connections at the bar, weighed on me; after a while, I felt like I had to be on the lookout every time I went out, and on the app every possible minute, for fear of missing out. This is inevitable, because almost nobody would make a good partner for you. You will fail and fail and half-succeed and have your heart broken and fail and fail and fail again, and then, someday, hopefully, succeed once and be done. That is what succeeding in relationships is.
With this in mind, it makes sense to make the process as easy as possible, especially in the early stages when failure is the most likely. If you date your friends, for example, you already know that you'll enjoy the social encounter (though you may not enjoy their attempts at romance or foreplay or something else); on the other hand, a stranger might not even make a decent dinner or conversation partner (let alone all the rest).
So all you need to do is make friends the way you normally would, and you'll have options galore, and it'll be fun to explore them as well. (Note of course that you shouldn't try to date every friend you make; the first cut shouldn't be the last.)
At first glance, it may seem like you have endless options for who to date; there are billions of men/women out there to choose from, wow! But you can't date all of them. Some are too young/old, some are taken, and some live very far from you in places you'll never go. Those are the default, zeroth cuts cuts that everyone makes.
Past that, you still have more options than you can reasonably sort through. The strategies above (going out, dating apps, and dating your friends) each represent a first nontrivial cut into the vast array of possible mate choices, by which we cull most of the unconscious space of possible mates down to those we analyze more carefully. To overstate things: "We take a handful of sand from the endless landscape of awareness around us and call that handful of sand the world." The first cut constructs the dating world for us, and it matters which method you employ.
A counterargument: you only have so many friends, so the pool of possible mates may be too small to find the right person. To this I say, make more friends! It's still the case that the selection process you go through in choosing friends is more likely to select for people you actually enjoy spending time with. Further, dating your friends sometimes is not an exclusive proposition; you can do this in tandem with other methods. Follow my advice, and you'll have more options, not fewer!
A counterargument: you may not be good at choosing your friends, and therefore will be searching a flawed pool of candidates for your ideal partner. If this is your problem, and you struggle to choose good friends, then to be frank, it sounds like you have deeper issues to work through. It may be a good idea to assess your life decisions (and, sorry, get your sh** together) before trying to make a long-term relationship work. If you can't find a good friend you can trust or whose company you enjoy, how do you expect to find a partner who is all that and more?
So with all this in mind, why not give it a try: Consider dating your friends!
* Though maybe not; some species have inverted intra-sex competitions. See e.g. this comment and links therein.