Only $3000? I hate to be pessimistic here, but I'm not sure that will even get you through Tech inspections! Add up the registration fee, one set of slicks, one set of wets, a set of seatbelts (they have to be new-ish), 2 fire extinguishers... that's at least half your budget right there. Hopefully that's not your whole budget and just the "car" budget, but still, it is going to be extremely difficult to build anything for $3k.
I was heavily involved in FSAE for 4 years. Honestly some of the most important work is not done to the car! Organization, leadership, sponsorship relations, scheduling, acquiring resources... that stuff all takes time and is just as important as building a car - you can't build a car without it! As said above, getting a car done as early as possible is one of the best things you can do. And that's surely not easy - you need to effectively manage your team members and their time, time (calendar), cashflow, and do plenty of testing.
As far as not having many resources, don't let that discourage you. My freshman year, we had minimal CNC access, no machine tools, a crappy tool chest filled with Taiwan sockets, and a small garage that had leaky pipes and holes in the floor. My senior year, we told the shop forman when HE could use the CNC machine, we had a Bridgeport of our own (fully tooled), three lathes, a new garage with exhaust suction and enough electrical power to run a small town, ball bearing tool chest filled with machinists tools, internet access, electronic keycard doors, and fresh concrete floors. Some of it was luck and timing, some was paid by the University and some by sponsors, but none of that stuff fell into our lap! And it definitely wasn't achieved on <10 hours a week.
Again fsae.com is the place to be, but use caution. Just like any internet forum, it's filled with retards who love to type just to hear themselves talk and may not have any technical knowledge backing the BS they're slinging. As an example, the people on our team who posted were the people that knew the least and did the least amount of work, and the guys running the team hardly had time to even read the forums, let alone register and post. I have also heard "xxxx team did it this way" as justification for way too many designs, in my opinion that's just plain ******.
Hopefully that's a bit helpful to you, best of luck to your team and be sure to post up some pics when it's underway!