Actually, 'a' means the cpu is built on the .13µ process.
Intel made two different 1600mhz cpu's. The P4-1.6 is a Willamette (256k L2 cache and built on the .18µ process), whereas the P4-1.6a is a Northwood (512k L2 cache, and built on the .13µ process). The P4-1.6a Northwood runs cooler and a bit faster than the P4-1.6 Willamette.
Northwoods only come in S478, but Willamettes come in both S423 and S478 flavors.
Asus has always been my favorite motherboard manufacturer. I would suggest a board that uses the i845 chipset, such as the P4B533 (or P4B533-C, if you don't need the onboard sound and other extras.) The P4B266 (or P4B266-C) would be another excellent choice.
And yes, you can certainly use your PC2100.