On my really old cupcake i can get about .3mm resolution. You can do support material, you just cut off the extra material at the end. small gaps and mild overhangs don't require support material (like that rabbit).

parts are made out of a thin tube of plastic. it's liquid and bonds to the layer below, then cools and hardens. they're claimed to be about 1/3 the strength of straight ABS (lego plastic). you can print solid, which seems really really strong, but most things are hollow, or just a thin webbing inside.

modern machines can get < .1 mm resolution. apparently the cutting edge reprap setups are exceeding commercial machines' resolution.

i've had nothing but positive experiences with makerbot support. I got mine very early, the design was still quite rough. i'll probably build another 3d printers soon, but likely a mendelmax. I'm just a lot more competent now.

That said, any makerbot would be an excellent first 3d printer. relatively cheap, good community and commercial support, everything is open.