The Dhayats are my favorite. I like their engine tech, and all they want to do is enslave every living thing, which is pretty laid back for a bug.
They're just kind of tricky at higher difficulties, since their econ is bad and all they want to do is build a million troops. Also they can't bomb that much since they really need population and don't want to piss off the hiveminds.
For gov I like to go Democracy > Despotism, since they can't afford much else. Democracy lets you bank some money early, tech up fast (armor troops, construction, missiles) and get rid of crap leaders, and despotism lets you 5 year plan out armor troops and not make every bug and lizard in the galaxy want to kill you. You just need to make things happen because the research + Dhayat growth penalties are brutal.
Naxxilians, Gizurians, Sluken and Hackinosh are cool too.