Again, you can read what I wrote for one. I started at 30, and I'm very happy with my success so far. Like, so much now that even if I never go a step beyond now I will have some bit of satisfaction in me forever.
It's both easy and not. Because once you commit yourself you'll be on the road to getting some success for yourself. But you have to stick with it.
I used to have the same feelings of anger and such regarding dating. I'd avoid thinking about it as much as I could. So I know what that's like. Just know that you absolutely can succeed, but you have to take it seriously. Or at least that's what worked for me.
It's actually a bit easier for guys than girls to start later. A 31 year old guy (like me) can spend time with a 21 year old girl, and it can feel completely natural, but even like the one 33 year old girl I dated shouldn't have too many problems. It's when you're in your 40s and haven't even started yet that you can have issues. But if you're started then no age is too late. (just my take on it) Well, you hear the stories of the suave & sharp 40 year old dating young 20 year old girls or younger. So, don't worry about that one bit.
Don't worry about a career or your own place. Don't worry about any of the shit you can't control. It's just better to proceed onwards. Don't forget about that stuff, but don't let it hold you back at all. Hell, I've met girls in their late 20's that still live with their parents, and they're not freak girls or anything weird at all. (unless you think that makes someone a freak, in which case you shouldn't)
Sure, try dating sites. Try anything. Get clothes you like, maybe some stuff you look good in while also feeling comfortable. Just one or two outfits is fine. If you think you look good in what you wear now, go with that. Clothes aren't super important by any means, but they'll matter to some girls a lot and every girl at least a little. It's like hygiene but less important. Literally one good top & bottom is all you need, but if you get into it you might find a bunch of stuff you like that boosts your mood just to wear.
Hair cuts are important too. Get the hair cut. It's not that big of a thing to do and you'll look better and you won't be worrying about your hair anymore either.
I'd say get your haircut, get whatever clothes and try interacting with people in real life or online dating to sort of establish yourself. Get over that step of fear and remember that girls are just people and everyone wants different things, as do you.
There's three parts of conversation, 1. someone that actually wants to talk to you, 2. getting experience talking to people, which will greatly improve your chances if you don't have a ton of 3. shared interests. That girl at work is just one girl and maybe you don't have much in common with her.