^Yes, it'll still be quick with a non-SSD. Just make sure you get a good hard drive. WD Caviar Black and Samsung Spinpoint F3 are the best deals right now.
I don't see why a wireless card would be a problem, as long as the router and card both have good range.
AMD is like G-D on this site. Really it just comes down to brand loyalty. AMD by its design as a budget CPU (the roots if the brand) runs hotter than intel. However that is nothing that an aftermarket CPU cooler can not fix.
Do what? AMD just has a good market position right now. If Intel was offering chips that powerful at the same price, with such a good upgrade path, we'd all be recommending them instead. Go to any computer related forum and ask for a build below $800 or so, and they're going to pick AMD every time. Intel doesn't really have a huge advantage in terms of power/price until you get above $1200 or so. Further, AMD's current processors will most likely be compatible with their next gen motherboards, but Intel is completely killing off their current sockets, so AMD's upgrade path is significantly better. It's even possible that the upcoming llano chip will run on existing AM3 boards.
And no, they're not "rooted" in budget systems. Back when the Athlon first came out, it kicked the Pentium III's ass nine ways from Sunday. Athlon XP vs Pentium 4 wasn't even a contest. And if you do some research, Intel has had to copy or emulate a lot of AMD's technologies to keep on top.