I have a v1.0 xbox, bought it the day they released in the US. I've never had problems with overheating or really, any problems with it at all.
I did softmod mine, which is, modding it without actually using a chip, but using a hacked gamesave that boots the Xbox into linux, thus allowing ftp access to the system and installation of all the same stuff you can do with a chip. However, softmodding isn't for everybody, and if you're planning on going with a bigger HD, you'd probably be better off using a chip, as HD setup is easier this way. I kept the stock HD and filled it up with emus and games, so it worked better for me. Chipping is also better if you have any intentions of playing on XB Live.
Personally, I say, save yourself a few bucks and hunt down a used one. If you've just got to have a new one, you're probably better off buying a premodded one. The price is a bit steep, but this way you don't have to deal with the hassles of the newer units.