Are you planning on using parts from your old computer?
I'd say to at least go with DDR. You're going to be disappointed if you go with anything less. DDR memory doesn't cost any more than PC133 at this point, and motherboards cost about the same. If your PC133 isn't good quality CAS2 stuff (i.e. Crucial) you'd want to upgrade it for overclocking anyway, so you can reach higher FSB's at higher memory timings. So all in all, I'd say stick to DDR, Crucial DDR at that, if you want to overclock.
If you want my recommendation, I'd say a 1.1 GHz Morgan core Duron is where it's at - it packs SSE and hardware prefetch that a TBird doesn't have. I'd say you're likely to get 1.3-1.4 GHz out of it. Pair this with an Epox 8KHA+ or a Shuttle AK31r3. The Epox should be in the sub-$125 US range and the Shuttle should be in the sub-$100 US range. Both great boards..... I can attest to the Shuttle.
And make sure to get a dang good HSF unit. You won't regret it. I'd say go with a Thermalright SK6 or a Millenium Glaciator II, both are relatively inexpensive for how well they perform (the glaciator being the quieter one, the SK6 performs slightly better when mated with a Delta38 or YSTech40). If you wanna go for the Rolls Royce, grab an Alpha PAL8045, with about a 50-55 CFM fan. It's relatively quiet and it's as good as it gets for aircooling.
Hope this helps.
SB