You can get sheet lexan from Ebay. I'm not sure about 'Home Depot', I'm in UK. Also, bear in mind that when you form it, the sheet is being stretched so it will thin out. So i would recommend using a 2mm lexan for a 1:10 scale. It all depends what you plan on making. Perspex can even be used in some applications like spoilers and splitters. But with Perspex, if it gets hit from a crash, it will shatter. Foam block may work, i've never tried, but as you say, i guess it may lose its shape when forming. I highly recommend Balsa wood for smaller stuff like bodykits, splitters and stuff. Bigger things, You want something farely solid and easy to mould and shape. MDF is an idea and im sure you can get it in brick form, not sure where though. Would be a nightmare to work with though. If you do decide to go the MDF route wear a face mask!

Also, a Dremel is the hobbyists best friend but you will need a steady hand. The more precise you are and the more time you take doing it and getting it right, the better the result.

In all seriousness though, See what the biggest chunk of balsa you can get is, and even use wood glue to make bigger pieces. use a dremel to get the shape you want then use wet n dry paper to get it completely smooth. It's also worth noting, the thinner the lexan you use, the more detail you will get. The thick the lexan, the stronger. Its a fine balance.

If you want to do a whole shell, Maybe try doing it like a real car... Panel by panel. Bit of a pain, but if you get it right, you could end up with something truely amazing.