Rules will vary from place to place, but most of them are just variations of what I'm about to tell you:
1) Goggles:
The *exact* requirements vary, but in general it's paintball goggles or any goggles with a balistic-proof rating of whatever is required by the field (the rating is stamped on the goggle itself)
http://blog.safetyglassesusa.com/safety-tips/how-to-identify-ballistic-rated-eyewear
Typically, the ANSI one is sufficient for airsoft although I've known a few fields to up their requirements for insurance purposes (although they seem to revert that change after they realize that airsofters aren't going to pay > $100 for new goggles just to play at their field)
If you're playing indoors, you'll want some sort of facemask and possibly a helmet.
2) FPS (feet per second muzzle velocity):
Also varies from field to field, but you can expect < 350fps for indoor games and anywhere from 375 to 450 for outdoor games.
3) Honor System:
It's not paintball, there's no mark that's left to show you've been hit so everything is based on the honor system. If you get hit, call "OUT!" put your hands up and walk off the field. Usually the game go pretty quickly and offer "X respawns" depending on the game type and is not worth trying to cheat.
On that note, people know if you've been hit too -- you'll most-likely flinch when you get hit and if ppl see you not calling your hits, they'll let it slide maybe the first or second time, give you verbal warnings afterwards and if you continue to think you're airsoft Rambo, then you'll either be left out of games, or people will continue drilling you with full-auto shots until you yell in pain (we play semi-auto only for indoors and maybe some full-auto is allowed for outdoors). Yes, we can be vicious when you don't play by the rules.
That said, we're not gonna call you out on stuff if it hits you in the vest or shoes and you can't be blamed for not feeling the hit in the heat of battle, but to be honest, a thin-ish/small vest to carry extra magazines and maybe a thin-ish long sleeve shirt is probably all you want. You want to fear the pain to feel the rush. If you wear full, thick armor from head to toe, you're won't be having fun :)
4) Equipment:
Does it matter? Mmmm...not really. The bottom line is: any gun that shoots 350fps is the same as any other gun that also shoots 350fps. So it's mostly about personal preference of aesthetics. That said, you will find that armalites (M4 variants) are the Honda Civics of airsoft guns and there's a lot more aftermarket parts/accessories for than if you were to use a SIG552, for example. Also, much like real guns, the longer the barrel, the better the accuracy so while muzzle velocity might be the same, an M4 with silencer hiding an extended inner barrel will have better groupings than an MP5 that's also shooting 350fps, gnome sane!?
5) Bolt action sniper rifles are cool!
Yes...yes they are, and that's why I have one. But please don't operate under the illusion that you're going to snipe someone across the filed without them touching you. Due to the FPS restrictions (typically BA sniper rifles have a slightly higher limit -- typically +25fps), BAs aren't going to outrange other guns by much (10' maybe?), but you would have to be at max range in order to take advantage of that. In most fields, your engagement distances are close enough that you won't be able to really outrange your opponent. So if you're just starting out, I wouldn't get this as your first gun because you won't be having fun with it. Mine is just a display item more than anything. I also sometimes fap to it (hey, don't judge me...)
6) Where to play?
I understand that you're in the US according to your profile, so any fields I name probably wouldn't mean anything to you, so you're on your own on this one.
7) Starting out:
Do so research/reading on the brands of guns. Waaaaay back when I started, there were really only 2 brands for AEGs (Auto Electric Guns): Tokyo Marui (TM) or Classic Army (CA), but in the last 5 years, a lot of cheaper Taiwanese brands have flooded the market and brands like TM are really hard/expensive to obtain. G&P, Magpul PTS, and KWA are all decent brands with good quality and pricing.
EDIT: starting out, you'll probably want to get a (ONE**) high-capacity magazine (or hi-cap). It's basically a magazine where you can pour in 300ish bb's and there's this gear at the bottom that you can wind to load up the mag again. A hi-cap = 300 rounds = $40. I run low or mid-caps which has much less capacity, but the reload process is much more fun and makes it much more realistic (also teaches you to not be as trigger-happy). Low caps = 40 rounds = $20 each and Mid-caps = 80 rounds = $35+