Discoverability is probably the second biggest hurdle when it comes to developing a game (the first is actually having something to publish)
So, title question. I know I could try to throw money at Instagram, TikTok and Youtube (know your target audience), but I think using their built-in advertising is more likely to miss than hit. Youtube is even more problematic, as a significant portion of people smartly avoid their ads (either with extensions or watching from piped or invidious).
Maybe paying to be on top of itch.io might work somewhat? I'd like to know from someone who did that, what was the turnout (number of sales/downloads per number of clicks)
One thing I think about is getting in contact with a number of small-ish (2k or less followers) content creators and work out a deal - free copy of the game, make a video being honest about it, leave a referral link for viewers to buy.
A problem of mine that I'm aware of is that I don't have much of a social media presence, not even Discord servers, thus I completely lack any sort of "organic digital voice".
I really want to know what are some decent strategies that a solo person could attempt to get some attention for their own game, and maybe the prices/budgets needed.
Guerilla style. Just never STFU about it on public spaces. Show it. Make a demo. If you're balzy, encourage some piracy of it. It might be annoying, but it works.
Go down so hard on the never STFU that I become second only to the Todd Howard selling Skyrim meme.
Not looking like an obnoxious moron probably helps, as Daniel Fox (author of Zweihander RPG) comes to mind as someone who did exactly that kind of "never shut up about it", to the point he got banned from a forum. It certainly brought attention to the game, but I don't think he'd manage to pull it off a second time.
He was also the main reason behind bringing down The Trove, but that's another story.
Haha, if you just stick to informing about your game(s), and not making it personal if someone has mean things to say, and/or oversharing your personal life, I don't think you have to worry about anything other than the occasional "I don't even wanna try it because I see it everywhere" person.