I always take the Egg first and a few skirmisher to quickly colonize and then mass assailants.
Actually, Vasari skirmishers suck. In terms of bang for your buck, they're actually one of the worst units in the game. Their only redeeming feature is reintegration, which must be researched, by which time you should be getting assailants anyways.
I try to get three civic labs for lava, ice, (as needed) and enslaved labor...
Enslaved Labour isn't necessary. It takes a while for that discount to pay off, and often times it's not worth it. I often get the upgrade that increases salvage efficiency then scuttle my civic labs once I've researched everything I want.
And five military for subverters.
Six, you want to research their special ability...
1. Are transporters worth it or should I mix in some enforcers instead?
Transporters are awesome. Once you have some phase missile research done, their strike craft are easily the best against frigates. They are expensive, though, so you'll need to use them carefully and not get them killed. Don't risk the transporters if you can help it.
2. I have pretty much completely shunned Overseers... am I missing something worthwhile?
Yup, they're your primary healers and invaluable for keeping capital ships alive. Also wickedly effective when combined with a starbase.
3. I have become more stingy with my research since my Advent thread but, besides important units, phase missle upgrades, and the occasional shield/hull/health upgrade as extra credits permit, are there other important things that I'm missing?
Don't get the shield upgrades as Vasari (or TEC, for that matter). They're too expensive and offer less than other upgrades. A better choice is the armour upgrade.
As far as late game tactics go, I tend to get a Skirantra then Kortul and phase stabilizers so that I can pretty much bunch everyone into a large victory fleet and mop up. Still mostly assailants and flak and SC ideally with full phase missle upgrades and the Eggs nanite bomb leaving caps in it's wake.
Sounds pertty good.