First of all, congrats on getting your group started! Taking the first steps of forming a group can always be a trying process... kudos for giving it a go!
One of the first things can really help getting started is finding ways to get organized early on. Coming up with the tools to manage your members, plan your events and get the word out about everything you do can be tricky.
I'd say the best way to get a jump on this: set up a group home page on a fundraising website. Many of them are free to use and can offer new groups amazing tools to organize, find new volunteers and raise awareness for a cause (regardless of whether you actually want to fundraise). Some require that you have non-profit status to form a group, but plenty others will give student groups, church groups and other groups without non-profit status some awesome ways to help get your group off the ground.
For example, one good site to help new groups is GroupSpaces (www.groupspaces.com). They offer plenty of tools to help get groups off the ground, including some event management functions that let you create events, as well as managing your members. And if you're interested in fundraising for your group eventually, they can link to your account and charge 2.5% of donations received (while some other sites charge as much as 5%).
Another good option would be Empowered.org (www.empowered.org). It is a bit newer than GroupSpaces and their platform is geared more towards social action, but are open to all small groups, regardless of non-profit status. Also, they offer plenty of solid tools to help new groups, and give groups the ability to create specific volunteer activities and events for each group (which GroupSpaces doesn't do). And if you ever were interested in fundraising, they offer specific fundraising campaigns (and charge 1.5% of donations) - nice if you ever go down that road.
There are some other sites worth looking into - Mee