Adric was, to me, a quintessential geek -- a genius with an insatiable curiosity. He was one of the few DW characters I could personally empathize with. He was a KID, too -- not one of the grown-ups whose job is to be stupider than they might otherwise be in order to allow the Doctor to look as brilliant as he was. He was impulsive, but not stupid, and willing and able to improvise a decent plan of attack to deal with problems he encountered.
He didn't seem to get into trouble as SENSELESSLY as many other companions; being a kid excused many of his actions, and he demonstrated level-headed thinking and a willingness to learn and act under direction -- again, which other companions often did not.
All this changed, of course, when Peter Davison took over, though the seeds were sown in the preceding eps. Nyssa slowly took over all the Smart Companion tasks, leaving Adric to play (a rather unbelievable) second fiddle.
Adric worked best with the pseudo-family dynamic of the Doctor, Romana, and Adric. This was, I believe, intentional.
I therefore saw the slow shift -- taking Adric from "bright semi-adopted kid with a potential to adapt and learn ANYTHING due to his origin" to "token Rebellious Kid played off against Better Companions", as a disservice to the character I learned to love in the beginning. And his ENDING crystallized things back to that original character, his last lines echoing back directly to the original Adric: "Oh, now I'll NEVER know if it would work."
NOTE: According to a number of sources, behind the scenes there were other reasons for Adric's departure; apparently the actor had a drinking problem early on and was hard to work with. But as viewers, we don't see any of that.
My favorite (old series) companion was undoubtedly Leela. In addition to her obvious appeal to any young male viewer, the important thing about Leela was that she was tough as nails, afraid of almost nothing, and saved the Doctor on almost as many occasions as he saved her. (Has ANYONE ever killed a Sontaran with a simple melee weapon before or since?)
Romana and K-9 were my other top favorites, again because they brought a level of competent usefulness to the Companion role which was in general absent from most other companions, who were more foils and sounding boards than anything else.