D-76 sounds very familiar. Which stop bath you use or fix doesn't matter as long you get the right concentration and time. Used to be several brands. Stop bath is just Acetic acid with a color marker that change color when it is all used up. I think I used to use Kodak stop bath and Ilford fixer, but have no idea what is available now. Most of the silver end up in the fixing agent, so it should be returned for recycling. If you want to prolong the life of the film you can finnish with HCA (Hydro cleaning agent). Agitation and temperatures matter a lot, actually when you have learned the standard procedure you can influence the appearance of the pictures (contrast, resolution etc) with changes in temperature, time, concentration or aggitation.
If I remember correctly, Tri-X has less resolution than the T-Max, but sharper edge contrast, which makes many features in the film looks more distinct. The grain are also very sharp which can be an effect itself. Has something to do with how the developed silveriodide cluster, have forgot the details.
Read up before you buy the drum and spirals. It can be a mess in the darkness loading a sheap and bad one, while it can be just so easy. Have fun!