Another vote for Tri-X or Plus-X. But also Ilford HP-5+ and FP-4+ (ISO 400 and ISO 125 respectively). All are "old style" emulsions.(posted 8705 days ago)For developer, D-76 or Xtol (watch Xtol for caked powders, check the archives). Also Ilford ID-11 (basically the same as D-76), or for lower cost, Sprint Film Developer (also basically D-76).
For stop, I use 1/2 strength Kodak Indicator Stop. I can't yet bring myself to use just water. But any stop is fine if you use it, but I do recommend mixing half strength.
For Fix, I use Kodak Rapid Fix, but any rapid fix is fine (Ilford, Sprint, etc). I suggest settling on a rapid fix since there is some concern that modern films are not properly fixed with standard fix. I can find no recommendations from Kodak either way with regards to hardening. Ilford says to only use a hardening fixer for high temp (over 100F or 38C) or roller transport. Hardening increases the time required for proper washing. I do not use hardener with any film.
I do use a hypo clearing agent, and for that I use Heico Perma Wash, but most any of the ones out there will work, or just buy Sodium Sulfite and mix your own. If you use Tmax films a hypo clearing step is required for rapid removal of the purple tint.
For the lowest cost, look into Sprint chemistry. For film, buy mail order, and buy in bulk. Maybe even bulk load, but I find that too much of a pain for the savings.