Others have said that D-76 is the standard against which other developers are measured. This is true, in a way, but this sort of phrase seems to imply that D-76 is objectively better than other developers. That's not true, except in certain narrow ways. It's just that D-76 is, first, a very popular developer; and second, a good compromise developer. It does most things developers should do reasonably well, but not spectacularly well. Broadly speaking, developers can be measured by their effects on acutance (apparent sharpness), speed, and grain. D-76 strikes a good average on these three measures. If you want to sacrifice one of these to get better results on another, there are developers that will do so.
I've never used HC-110, so I can't comment on it from personal experience; but based on what I've read, I'd say it's not that bad a general-purpose developer. It's also got the advantage of coming as a long-lasting liquid concentrate, which may be preferable to a powder that you must mix to a stock solution and then (usually) dilute to a working solution. Depending on how much film you shoot, your D-76 could go bad before you use it all. HC-110 isn't likely to do that. If you think you're likely to go through your first batch of D-76 before it goes bad, though, it's a more popular developer than HC-110, which means you're more likely to be able to get help if you run into some strange problem with it.
Concerning Rodinal, it's another liquid concentrate, and it's got legendary keeping qualities. It's generally recommended for fairly slow films, though, (say, ISO 200 and slower) since it produces bigger grain than most other developers.
Ultimately, developer choice is very personal, and some people get very passionate about it. IMHO, it's best to start with something common and general-purpose, like D-76, XTOL, or HC-110, and move on to Rodinal, pyro developers, and other things later. Some people might move Rodinal into the first category or HC-110 out of it. Like I said, it's a subjective and personal matter.