Well, when I was first starting my anime club there were a few things that really helped smooth over the process, and would like to remind you of a few things as you get into it, if I may.

The first thing to do, and I'm sure you have thought, is to set up some sort of government with a few leader positions filled with responsible people (not just friends who ask, but people you know will do their job). Even if you only have a few members, set some sort of skeleton in there that you think will work. I run a pretty small and semi-structured club due to various reasons, but because of that I only have a vice-president. DO NOT DO THIS IF YOU ARE THINKING OF MAKING IT OFFICAIL. You will need more people by your side than just one if you plan on your club being successful, especally if you plan to handle funds.
Secondly, with your government in place, you will need a constitution. I had to have this spelled out to me by the person who helped me make my club almost a year ago. It's usually an overlooked step in club construction, but it helps greatly when order is in high demand, especally around a large number of members. The constitution should set up everything from election proceedings to funds handling and acquisition; from simple club rules, obligations, privileges and conduct, to membership and terms of office. You should outline as much as you can in this document, but keep it free enough so that you aren't operating stricktly bureaucratic. The form of leadership I use for my club is a constitutional monarchy, and I think it works just fine.
The third thing that you should get in order is how you will get shows set up. Many companies sponsor club advancement programs, some of which give out free shows or preview DVDs; I would advise joining as many as you can, and asking permition before showing titles in your club. For the sake of being a respectable club, I advise you steer clear of watching torrented shows and just use club funds (or your own) to buy boxes. This can be a problem, especally starting out, if you don't have any shows you currently own or any funds to buy them. If this is the case, DO NOT PANIC; breathe in, and breathe out. Ok. There are plenty of alternatives, such as legal streaming sites. Sure they may have commertials, but you have to start somewhere, right? Oh, and make sure you have the company's approval for each show you watch. Funimation refuses to recognize my club as a club, so as far as I'm concerned I'm just watching shows with a bunch of my friends privately.

If you have any other questions or concerns, please ask. The more collaboration, the better.