Honestly, not much. Half the work is done by other players. The first time I read the OP, I'm skimming for the most important information about the setting, then I'm heading straight for the approved character sheets. If the characters seem fun to interact with, I might join just for that. If the GM is approving overpowered characters with hilariously dumb backstories, that's a deal-breaker. Likewise, if the GM's own character gives me "main character" vibes, then they'd better be cooked to perfection. If the GM's character is basically godmodding in their own backstory, that's an instant nope. I am 100% reading everything in the character tab before I commit to pitching my own. Maybe that goes beyond the scope of the question being asked here, but I think it's an important part of how I decide if I'll play or not.
If the characters look good, I'll re-read the OP, looking for details I might have missed the first time. Primarily what I need are some consistent themes and tone to bounce off of. I like to make thematically designed characters, with appearance, personality, history and skills that make sense together. Uniquely original settings are great for this, but not required. Not every character in every story needs to grow and change, but I do like to include that, so if there's opportunity to create a character who's in over their head, that's also a plus for me. As long as I have a vague concept for a character in mind by the time I'm done reading, you probably have me.
Which leads into the other major thing I'm looking for: some kind of interesting conflict. I love a good dialogue between well-defined characters with different mindsets. Verbal sparring with precisely-chosen words dripping with subtext is the kind of thing that's hard to do if there's no kind of conflict going on. For me, the more complex the conflict, the better. I like it when characters with wildly different motivations can come together for something, though if that something is saving the world in some generic sense, I might pass. Sometimes, actually maybe a lot of the time, lower stakes and highly personal conflicts are just more interesting.
As for additional plot details... I don't mind if some aspects of an interest check are intentionally left vague to set up some kind of reveal later, but if it looks like the main thrust of the story won't be explained until well after the thread is underway, I probably won't sit through the opening fluff to find out if the GM actually has plans or is just making stuff up as they go. Other than that, not picky.
Setting is also a whatever. Worldbuilder's disease is a thing though. I'll read a good wall of text if it's written well and interests me, but that's a risk you're taking there. You could have the coolest setting on the forum but if nobody joins because TL;DR, it doesn't really matter. It's also a waste of a good setting if the characters, conflict and story are so boring that everybody quits. Easy 4th place for me.
After I read the OP and the character tab, I'm reading the rest of the thread. What the GM doesn't approve and why, and whether or not you agree with their decisions will tell you a lot about whether or not you'd enjoy their RP. It's all there if you look for it, and I don't think it's entirely unfair to draw reasonable expectations from it. I have a soft "rule of three" when it comes to the whole character design process. If I can't come up with an idea that I'm totally in love with after 3 cracks at it, or the GM shoots me down 3 times, I bow out. Likewise, if multiple people made characters that I liked and they all got shot down, I'll take my keyboard and go home, thanks.
I guess I could mention some 1x1 interest check specifics too. I read basically all of them—sometimes for my own sick amusement—but the ones I skim through most quickly are the ones with vague or done-to-death premises that demand smut up front, and/or give nothing but a list of pairing prompts and a list of kinks. I'm also a bit tougher on grammar when reading 1x1 threads. I've done a few good RPs with one or two players whose posts were basically an unintelligible mess, but I'm gonna need more than coffee to survive that if I only have one partner.
This post probably reads as more critical than I mean to be. I'll add a disclaimer that I'm not talking to or about anyone in particular. But I do think there's a lot of lurking going on here. It's "safer" to get sold on someone else's idea than to try and sell your own and be down in the dumps because nobody seems interested. So, to summarize all of this in a feel-good statement at the end, as long as your OoC is coherent and makes some kind of concrete promise about the kind of story you want to tell, and the characters you approve as GM are fun and interesting to play with, the actual A to B plot threads and micro level details of the setting don't actually matter to me that much.
