Corps to look at -- keep in mind, I haven't been in any corps except the one I'm currently in, so this is mostly based on what I've heard and read elsewhere. If you join one and they suck, there are no refunds from me.
PIRACY
Privateers - They just recently changed their policy so that new members must be 3 months old to join. But that was JUST changed yesterday, so it still might be worth looking into. If nothing else, keep them in mind if you keep playing. My opinion on the Privateers: many of them are annoying as hell. However, the concept of the corp is kind of cool. There's no central command, no power figures. They declare war on 30-40 alliances at a time -- which means that they can gank those alliances even in high-sec without getting crushed by the police. Basically, it's a growing anarchist piracy group. Easy to find people to group with for pirating, and I hear that many of them are actually good fighters and not idiots. The few idiots just happen to be the few that post a lot on the forums.
SniggWaffe - A piracy training ground that seems pretty well regarded by former members. They require a few specific skills that are not too hard to train up quickly, depending on your starting build. They also require a microphone, presumably for Teamspeak/Vent.
ANTI-PIRACY PVP
Ushra'Kahn [RP] - U'K is a roleplay corp that is primarily about anti-piracy PVP. They defend their area of space from known pirates, and operate on a NRDS (not red [hostile], don't shoot) policy, meaning neutrals will not be fired on in U'K space (at least not by U'K). They have a corp for new players (Kinda’Shujaa) where you go through a training program, at the end of which you can join other U'K corps.
The required RP is light -- it just means that any talk in the Local channel must be in character. However, their wars are sometimes RP based. U'K is a Minmatar alliance fighting against Amarr slavers. That means that ANY ship carrying slaves, even neutrals, is kill on sight. Even neutrals associating with slave-carrying corps/alliances are open game. MerchI (the corp I'm in) is currently associated with one such alliance. After attempting to maintain neutrality, our pilots kept getting shot down by U'K, so we're currently set to negative standings on them (meaning we're not in official "war", but if we see U'K, we start shooting).
PIE Inc. &
Auctoritan Syndicate (starter corp for CVA alliance) [RP] - PIE Inc. is a former CVA corp I believe, while AS is CVA's starter corp. Both accept young pilots, but due to roleplay restrictions accept only Amarr pilots (this may have been relaxed -- if interested, it's worth asking their recruiters). CVA is the primary opponent of U'K (Amarr slavers vs Minmatar freedom fighters) and they've been in a constant fight for quite awhile now. CVA is also anti-piracy, and they defend most of the region (Domain) that MerchI (corp I'm in) operates out of. If you'd interested in joining a corporation that belongs to an alliance, but not one that is so huge where you'll just be a meat-shield, joining CVA or U'K are both fine options. They're established alliances that hold their own space, but they aren't huge by any means. You're also going to find plenty of fights, both with the opposing alliance and with pirates.
GENERAL BEGINNER
Eve University -
Frankly, I'd suggest this route if you're having trouble finding a corp you like. Aside from those listed above and the one to follow, which I have at least a little experience with, I'm about as lost as your are when it comes to specific corporations.
Eve's a big place. I can suggest the major alliances to you that might have starter corps (D2, IAC, LV, AAA, IRON, FIX -- also GoonSwarm if you're a poster at SomethingAwful.com's forums) but it'd take some effort to actually track down the info on which specific corp you should contact. Most alliance websites have recruiting areas, but it's recruiting for CORPORATIONS for the larger alliance, not for players to join existing corporations. So if you want to join one of the big powers of Eve, start looking up their corporations and asking around in-game. Many corps should have recruit info in their profiles, but firing off an evemail to a listed contact doesn't hurt either -- worst case they tell you that there are no starter corps, best case they point you in the right direction.
But if you don't know just what you want to do yet, or you want to get a better handle on the game before joining an existing corp, or you just don't want to go to the work of finding a corporation filled with people you don't know working toward goals you may or may not be in line with, then join Eve-U. It's comes highly recommended all around, they'll help teach you things about the game (probably will end up knowing more than I do within a few days
), and will be able to help point you towards some corps once you feel comfortable moving on.
If nothing else, you'll have some players to group with for missions, NPC hunting, or fighting pirates. And you'll get some training in whatever aspects of the game you're interested in, so when you find a corp you DO want to join, you won't come off like an idiot.
INDUSTRY/PRODUCTION
Merch Industrial - The corp I'm in. We're focused primarily on mining and production, but we do have combat pilots as well -- necessary to defend our area of low-sec space. People are helpful as long as you aren't annoying. I've had several vets help me out, whether it was just asking questions about the corp, the game, specific questions about what ships to fly and what equipment to put on them, skills necessary for PVP, etc.
If you're PVP-centric then it's probably not for you. Most of our PVP is defending from pirates, and while we do a good job of it, it's not constant PVP action. Of course, once you're able to hold your own, you're more than encouraged to go out and hunt down player pirates. But at first, you won't do PVP really unless you're with a few other people.
So if you need constant PVP, look elsewhere. If you're okay with occasional PVP, or are into mining/production/NPC hunting/missions, consider joining. They accept all, which means I'm not going to vouch for you. You join and act like a jackass, I'm not going to defend you. Keep in mind, I've only been there a week. I like it in MerchI, but I'm
certainly don't have any strings to pull.
Also, if you join MerchI, you're probably going to want to do one of two things:
1) Chill in nearby high-sec Empire space, running missions and killing rats, until you can fly a decent Cruiser
2) Come down to our 0.1 home, but you'll have to be a miner at first and run like hell from both NPCs and player pirates, until you can fly a decent Cruiser
Because you're just not going to be able to defend yourself at all in a frigate, really. At least with a Cruiser, you can equip it to give you enough time so that if you do get jumped, you can get out of there to safety.
I'll try to add to this as I go, but a good way to find out corps to join, truly, is to read the forums. The recruitment ones have bad signal:noise ratio but they're worth skimming. But read the Corp, Alliance and Org Discussions forum to get an idea of who the major corps/alliances are in Eve, and who you'd want to join with. Then check their info, their corp's info, and the alliance's info in-game to see what you can find. At the least, you can usually find someone to contact that can point you in the right direction.
Also, I'll gladly toss 3 mil ISK to any starting 2+2ers who want some help getting started. All I ask is that you don't blow it on high-priced equipment for your ship. Use it to buy a better ship, use it to buy skills, etc. Basically, use it conservatively and you can feel a bit more comfortable, knowing that if your ship gets crushed that you aren't going to have to mine for 3 hours to replace it. If you decide not to extend the trial, just toss the remainder and your goods to me. If you do extend, then help some other new player down the line.