I shot "the old Tri-X" at 1600 with good results. With current Tri-X I find it depends (I find the same thing with TMY to a greater extent) very much on the light. In daylight, say an overcast day, I can still use 1600 and get great results. But in tungsten light 1600 is a bit thin and I prefer 1000. 1250 is a good compromise.
If I had to standardize on only one developer it would be Diafine. One of my favorite combos used to be Plus-X at 400-500 in Diafine. I preferred the results to Tri-X at box speed in D76. Current medium speed films don't seem to do as well, by which I mean they don't get the same speed increase though they work fine. FP4+ is more like 200.
I use Diafine now mainly for two films: Tri-X when I want 1000-1250 but don't need Delta 3200 speed, and for Pan F+. It's a great developer for Pan F+ in my experience, both taming some of the contrast by moderating the highlights and giving a small but useful speed increase. I shoot this combo at EI 64. Though that's only 1/3 stop over box speed, most people using other developers seem to shoot it at 32-40 so it's more like 2/3s to 1 stop.
I've posted this before, but I gave my wife's parents a mounted and framed print of roughly 15" square of this photo for Christmas. (I shot this at the beach house they rented for a month in 2011, while we were staying with them.) They put it over the mantle and wrote a thank you card saying how much they like it. The print I made for them is somewhat darker than this rendering. Pan F+ in Diafine, EI 64:
Apalachicola Beach 1 by Roger Cole, on Flickr