Transmission options for LS motors, any advice?

[Salty]

I am in the research stage of my build. I am reading many threads about high HP cars, race cars, and way crazy builds and realizing many of them do not reflect what I am looking to get out of this transmission.
Here is some background of what I have and what I ultimately want.
1968 Firebird, currently no motor or trans, 10 bolt GM posi rear end(think they are 3.73 gears). It is a clean palette so I want to chose wisely for my build by asking questions and doing lots of reading.
What I want to end up with is: 68 Firebird with modified suspension, brakes, LS2(or similar engine, 400hp or so), and a automatic that will reliably handle this 400hp. This car will be a daily driver for me 7 months out of the year so i don't need a huge stall but I do want to have some fun!
What trans would you suggest and what models of cars can I find this trans?
Is a 4L60E strong enough for me or should I just start with a 4l80E?
Any advantages to either of this transmissions?
Any thoughts on the 6 speeds that come in the newer G8s and such, are they decent?
Thanks,
Salty