I'd like to find out if placing a smaller wheel size would help in any way to get a faster acceleration time. also how much it would cost to get a lightweight wheel set.

We would need a lot more information to answer your question. On many cars, you can't go smaller due to brake clearance issues. What type of car (make, model, year) do you have? What size are you running now? Were you looking for an all-season or Summer only tire? Is this for street use or track?

2000 ford focus se, i'm rollin on 15's, i'm thinkin' 14's all season, and it is for street use