Pros: A corp, especially a small corp of good players can give you great support and really accelerate your learning of the game. This has been my experience with my Corp with <20 people (active players). We have a blast, go on roams, and they've really upped my play quickly. They are associated with Goonsquad.
Cons: Being associated with Goons has been a really, really mixed bag. They can be organized, such as the war effort where they are crushing it.
But around their own home base, enemies gate camp all the time, and they're a Charlie Foxtrot. If you dare complain, you get laughed at at best, or told to go join Horde. This wasn't by some minor player either. Don't get me wrong, are some Great Goons, but it is an old, old Alliance. Think "Old Republic"... and there's a lot of rotten players in there too. I suspect you'll find that in all of (the alliances) though.
Pro: It gives you people to quickly, and easily, join a fleet with. This can be both fun, and profitable. They also give you the ships and the fits, so you aren't out-of-pocket to do this. They also have a huge amount (overwhelming really) of info on character building. Luckily, they also have chat channels where you can chat and sort out some of the information overload.
Con: You are an Instant Target. Regardless of what group you join, they have Enemies. Once you join them, you have Joined a Gang. All their enemies, are YOUR enemies, and will gank you, just for being associated. And for fun. In theory, your Alliance supports you against your enemies; in practice, unless you are in a fleet, you are a target for their roams (fleets) and you are unlikely to get any help if jumped. But if you are on a Roam, neither will they. Usually.
Take all of this with a Shaker of Salt. It is my Opinion, and Mine Alone. I've been playing about 3 months.