Check out the Sticky Threads at the top of the
Cases & Cooling Forum for some helpful leads.
The heat output of your 1GHz Thunderbird is about 49W maximum. The 1600+ and 1800+ are 56W and 59W respectively with the Palomino core. AMD will begin switching the 1700+ and higher to the Thoroughbred core, so if you get something above a 1600+ there is an increasing chance that you'll get a Thoroughbred. Because the Thoroughbreds have such a high wattage-to-surface-area ratio due to their small core, you would be wise to get a heatsink with a copper base to allow for this possibility if you're buying a 1700+ or higher, since that's what AMD reportedly recommends (copper-based coolers for Thoroughbreds).
In general, a heatsink that takes an 80mm fan is desirable for a low-noise setup that cools ok. If you were getting a 1600+ then an SVC
GC-68 would be hard to pass up at only $5.99. Since the GC68 doesn't have the copper base that you'd want for a Thoroughbred, it might be better to get a Thermalright
AX-7 in that situation, along with a low-noise fan like a Panaflo L1A ,or maybe an adjustable-rpm fan from YS Tech or Enermax.
If cost is no object, Alpha PAL8045 or Swiftech MCX462 would be slick. PAL8045's don't fit all motherboards, fit list is
here.