This is a classic, middle-of-the-road, standard combination used with great success by many photographers. It has a very nice look.
Tri-X, having a long toe, benefits from slightly increased exposure of 1/2 to 1 stop if you desire good shadow detail. Examples might include product shots of black leather goods, dark blue suits and farm animals with brown or black coats.
I personally have always had (for 40 years) an aversion to HC-110 because it has a nasty habit of dying without any warning such as a dramatic color change. I have had friends lose an entire 18-reel stainless basket of 120 film due to this anomaly.
My recommendation for a similar developer would be Kodak's D76 or Ilford's ID-11. Slightly increased dilution (such as D76 @ 1:3) will yield longer development times, increased sharpness and very slightly increased grain.
I would not venture a proper development time. That depends upon your metering technique and your kit of assorted equipment, from light meter to lab thermometers to timers to lenses to enlarger to water quality, etc. Honestly, experimentation is really necessary.