What are my options for annealing brass in the $150 and under range?  

I don't know of any machines that are in that price range, but I could have missed one.

I did find Anneal Rite II. I don't think that is much better than the 1/4" drive deep socket & a drill.

If I did go the deep socket route, what sizes would I need for .308 and 6.8SPC?

There is a thread already posted up about it ( diy annealer thread )

If your were inclined to build your own auto annealer, $150 will get one built like mine ( http://youtu.be/0-C-i0Kr2jU ) but mine cost a lot less as i had a few bits n bobs already. A few of the other guys have built some great ones based off mine.

I have a few more diy builds in the works, i just gotta get some free time.

For well under your budget you can get these -

A cookie sheet filled with water
Tempilaq indicator
Propane torch