I shoot Tri-X at 200-250 and develop it normally, as from everything I have seen this is the true speed of Tri-X. But being Tri-X, it's not going to make a rat's behind of a difference either way because....it's Tri-X. Very flexible film. However, temps and times are not so flexible. You should have 3 thermometers (I used only one for a while and it was a royal PITA, but it worked. Sorta) and keep the temps as close as you can.
For developing you need to be within a degree or two at the most. Stop bath and fixer are not as critical because the developing has been done, but you still want it as close as possible. Keep your agitations consistent too, and follow the film's instructions for your developer. This is something I failed to do on a recent outing w/ Fuji 400 Neopan, and you can see the before and after effects in a thread I have here on the forum. When I used Fuji's agitation protocol it made a HUGE difference. For Tri-X, (this is for D76, but I think it's the same for HC-110) Kodak says to agitate initially for 5 cycles, or 5 complete agitation cycles. I go with 30 seconds initially. Afterwards, Kodak says to use 5 seconds of agitation every 30 seconds, so I do 2 inversions every 30 seconds. I don't do anything the last minute, although now that I look at Kodak's recommendations I don't see that anywhere. When you agitate, use a sort of rolling or swirley motion.
Follow Kodak's directions for your particular developer (I recommend D76, but lots of folks use what you have w/ success), keep your temps on the money, agitate properly and you will get great negs. Obviously, you need to have complete darkness for getting the film into the tank, and your film needs to be metered correctly on a camera that exposes correctly. Then you get this: By the way, I goofed on this developing and used the times for 1:1 dilution for Tri-X in D76 and accidentally gave it the same times w/ full strength developer. Hey, it's Tri-x! Yes, it's a little grainy, but man, it made a nice print.
When you develop it correctly it comes out like this: