As for upgrading with a pentium 4, a 1.6 chip would most likely use a different socket, and besides that there have been so many upgrades that it would be a large hinderance to not get a new motherboard. So if you get AMD or Intel, you'll have to get a new motherboard in either case.
Basically, because of architectural reasons (Shorter pipeline, better floating-point unit) Athlon 64s end up being a decent amount better than Pentium 4s for games. As for stability, my current Athlon 64 system is rock-solid. Really, at the current time, AMD is barely any less reliable if at all.
And if you do go with AMD, you might as well go with socket 939 (The newer one). One main difference between socket 939 and socket 754 at the moment is that socket 939 supports dual channel memory, which is a bit of negligible boost in performace. In addition, in the future, socket 754 will only be used for budget 32-bit CPUs, while 939 will be where new 64-bit CPUs are released. Oh, and in the same sence, when daul-core CPUs start coming out next year, you'll find them on socket 939. Also, of greater use, is that socket 939 has 90nm CPUs, while spcket 754 has only 130nm CPUs. The difference here is that 90nm ones end up putting out less heat.
Oh, and for those curious: (In real dollars now)
ASUS k8v-MX (bulk) SKt754FOR ATH64 VIAK8T00 W/AUD $93
AMD RET-ATHLON 64 3200 SOCKET 754 W/HSF $193.58
MAXTOR 0EM 120 GB IDE 7200 RPM 10MS ATA133 8MB $73.85
VDATA DDR NON-ECC PC3200 CL2.5 512mb 400 MHZ $58.06
DVDRW-OEM BENQ DW1620 BLACK16+/- DBL LAY $57.23
PANASONIC 3.5" 1.44MB Black $9.97
Microsoft DSP Windows XP Home w/Hardware OEM $87.24
ANTEC SLK2650BEQ CHASSIS ATX CASE BK ATX12V 350W P $83.08
TOTAL PRICE: $692.00
So yeah, I'd go for socket 939. A 3200+ on socket 939 is $225, but read above for an explanation. As for a motherboard, I'd go for something based off NForce3. I've heard good things about the MSI K8n neo2 platinum, and I've never had any issues with the neo1 platinum I have. Also, I've heard decent things about Gigabyte's board. If you're going for socket 939, then you might as well buy a pair of matching memory sticks, so you can take advantage of dual channel. Oh, and I'd recomment at least a 400W power supply for your system, just in case. 350W might be adequete, but it's sort of iffy.