There are lots of great systems out there. As much as I love 4e, tactics games don't play well online. I use 13th Age for that. It's got some silly narrative mechanics that I think you're better off dropping, but I love the core character rules, especially the background/skill system.

Strike! is a little game that tries to fix 4e ,but keep it a tactics game. It splits up class and role as two different choices.

I haven't played it, but there is a generic fantasy version of Fantasy Flight's Star Wars RPG, the one with the dice pools. That's on my list.

Shadow of the Demon Lord is supposed to be good and also vaguely in the group of 4e descendants. I haven't played that one yet either.

Definitely don't stick with D&D if you can help it. It's a fantastic place to start, but 5e is shallow. Hell, if you want interesting, try AD&D. Not the best game, but full of interesting design.