If you’re going to buy refurbished, I HIGHLY recommend you don’t do so online. Most places that sell refurbished offer some sort of limited warranty, and since you’re buying a machine that used to be broken, the odds of getting a lemon are marginally higher (hence the lower price - added risk). If your Box breaks, it’ll be a lot easier to return it to a Real Live Store than to some place on the 'net. That being said, eBay often has used systems selling for $120 or less. With that big a savings, it may be worth it to you to risk an online purchase. Your call. For the record, I picked mine up refurbished at a GameStop for $150, and am quite happy with it.
At any rate, the aforementioned price drop is already in effect - new systems now go for $180, and I believe that still includes Sega GT 2002 and Jet Set Radio Future (the former is okay, the latter is pure joy). Refurbished systems generally come with no games. Then again, you can pick up the Sega GT/JSRF combo disk for $15 used, so the pack-in isn’t all that much of a selling point. Be careful with refurbished systems, though - many of them sell with the old controllers, which suck mightily (they’re large and bulky). The new Controller S (which is what the new systems now ship with) is a great controller. Make sure you know what you’re getting, and handle the controller to make sure it’s comfortable for you (I didn’t, and got stuck with the Big One; not a huge deal, since I was going to buy a second controller anyway, but still…).
As far as wireless, I have no experience with XBox wireless controllers. However, I do have some Wavebirds for my GameCube, and they are absolutely wonderful. No delay, no problems with the signal cutting out, and no worries about something getting in the way of an IR port - they’re radio, not IR. So excellent wireless controllers are at least possible in theory - whether or not there exist any excellent XBox controllers, of course, is another matter. That being said, the XBox controllers have 8’ cables, so wireless is less useful than for other systems.
[gushy pro-XBox aside]
I am so glad that the XBox appears to have been designed by people who actually play games, and listen to gamers. Long controller cords, writeable hard drive, 4 controller ports, good controllers (the S, not the behemoth that was the original controller), sensible configuration menus, tear-away controller cables for when someone trips over a cord… Just about every gripe ever made by a gamer seems to have been heard and addressed by MS. Even the Giant Controller of Doom fiasco is excuseable, given that it was in response to the oft-heard complaint that most controllers are too small for American hands. Their system is by no means perfect, but they did a damned good job, considering this is their first stab in the market. I hate a lot of their PC software with a fiery passion, but the XBox is a first-rate piece of machinery.
[/gushy pro-XBox aside]
Anyway, happy hunting. Let us know if you need help picking out games. 
Jeff