There is ample parking at Wesleyan. As a freshman, you get the short end of the stick—but it's not that bad. Vine Street is the main parking lot freshmen are allowed to park in, and it is a short walk away from most freshman dorms. If you live in the Butts, a program house, an apartment, or a senior house, you will most likely have your own parking lot or open street/driveway parking.
You have to buy a parking pass, which costs $50 per semester, but it's really best to buy it—Wesleyan cracks down on illegal parking, and you can get stuck with some pretty hefty fines. As to whether you should bring your car to Wesleyan or not, it is useful to know someone with a car, but if it is yours, then lots of people will ask you for rides. Thus, it's definitely better just to make friends with people who have cars and then mooch off of them.