D-76 is a superb general developer. If you want to minimize grain, then use stock. Also, as suggested, give XTOL a try; another outstanding developer. I use both at 1:1. XTOL seems to have more perceived sharpness and an edge on shadow detail, D-76 a tad softer. At print viewing distances, I can't tell the difference. Edwal FG7 isn't mentioned much -- I used it a long time ago; it's an underrated general developer that also works well -- easy to mix and use.
I would've suggested Rodinal for use with the 100-125 range films (pull them about a third stop, as there's some loss of speed with this developer) -- it leads with an open and wide array of mid-tones. Although you state that you'd prefer to minimize grain, give it a try sometime; it's a different look. Colin's suggestion for TMAX developer is a good one (DD-X from Ilford could be an alternative). I used HC-110 a few times, years ago; it's a fine developer, but not my cup of tea for 35mm. It's outstanding for medium and large format. There are lots of choices (as well as numerous exotic concoctions better reserved for larger film format sizes, as you'd begin to see clear differences in personality). Everyone has personal preferences as to look and feel; one is not "better" than the other -- far from it.
For 35mm, I use XTOL the vast majority of time, and have D-76 and Rodinal on hand, depending on the projects on which I'm working. I rarely venture away from Tri-X; sometimes I'll use Neopan 400 and Plus-X. I keep it simple, and focus (no pun intended) on the final image outcome later.
Enjoy.