1. It doesn't really matter. But if you get a v1.6 (or 1.6b) xbox, it takes some more soldering and you'll need a special type of bios for the xbox. There's been many complaints about the bios for 1.6 xboxs. I don't have a 1.6 xbox so I don't know how true these complaints are. I'm not sure if there's a bios out for the 1.6b xboxs yet. I suppose you're better off buying a used xbox b/c it's cheaper and you may be more unlikely to get a 1.6 xbox.
2. Any of the new modchips out are good, Xenium, Xecuter 3, SmartXX. Xecuter 3 has more features, but generally cost about $10 more than the other chips. I have a Xenium and have no complaints.
3. Going on Live with a chip (as long as the chip is off) is somewhat questionable but most likely safe. Team Xecuter believes in the "marriage theory" (explained here -
http://www.xbox-scene.com/xbox1data/...EFqmSCCwfD.php ), and if that is true (which it probably is), Live won't be a problem. Kai works great with a modded xbox as some programs (XBox Media Center) have some features for Kai (never tried it out though, sorry I can't provide details).
Hope this helps. Installing a modchip is fairly easy so you won't be getting your hands too dirty.