Hi. I can't really tell you about anti hiigaran tactics, because Im Hiigaran only player (I just love them). But I noticed that Hiig corvettes are BEASTs. AI usually overextends a little and I found the best way to deal with them is to move flagship/mothership forward and setup a kill zone around (def turrets), let fighters and corvettes fall back until they are in the killzone and then send them to support. That killed those corvettes easily enough.
Even on easy, complex AI is always little ahead of you at the beginning. I think its because AIs are sick micromanagers (watch out for focus fire). I usually catch up on them by the time around first destroyers.
This is only my opinioin though, but i think Hiigaran are a little bit stronger and tougher than others. On the other hand Vaygr missile frigates have a longer range than anything but capital ships, use it.

Good luck and have fun.