For stability issues, get an INtel CPU on an Intel chipset. Even better, get an Intel CPU on an Intel motherboard. Those motherboards have improved tremendously over the last few years. There was a time when I wouldn't even consider touching one of those motherboards, but now they're practically my number one choice. The only reason why I'm not using an Intel board now is because they lack the overclocking abilities I want because I'm using a watercooled setup. (something you've said doesn't interest you)

If I wasn't using that watercooling rig, I'd change back to an Intel board in a heartbeat. The board I used before the one I'm using now (an Aopen - also a very stable board) was an Intel and it was hands down THE BEST board I've ever used. Rock-stable and with all the necessary integrated peripherals. Alll the bells and whistles you could ask for (including 1394 which is kinda strange since intel opted to not implement that into their chipset) are now included on those motherboads.
The best bang for the buck are the i865 Springdale motherboads right now (and for some time to come).

I would also like to add that I'm not that big a fan of Asus motherboards. I've used them a few times with varying results. Sometimes very stable, other times nothing but throuble and instability. (I also had that issue where I had to solder that jumper wire onto the motherboad). Abit is even worse. The best motherboards that I've used that aren't Intel motherboards are Aopen. I've used 6 different models of them myself up till now (all intel chipsets), built hundreds of systems based on their motherboards for other people and have never encoutered any problem.

For CPU, get an Intel 2.6 or 2.8Ghz, but make sure it's a Hyperthreading CPU. Those run on 800Mhz and don't cost that much more than the "older" models.

For RAM, make sure to get DDRAM-400 memory from a good brand like Corsair or Infineon. Don't bother with ECC Ram's : the i865 doesn't support them. (in fact that's practically the only difference between the i865 and it's much pricier bigger brother the i875). Remember that with an 800Mhz bus CPU, you'll need to install your sticks of DDR-400 RAM in pairs again to be able to use them to their fullest potential !! (just like we had to do with Simm's with the Pentium 1's)