How about an old fashioned 2 groove Saginaw 4 speed. You can usually pick them up for 200 250. A rebuild kit runs 120. New forks might be 80 or so. About 450 rebuilt at the top end if you do it yourself (the sag is a fairly straight forward rebuild and good for a first time builder). The 2 groove comes with a 3:11 first gear. As for strength, not terrible. You will hear lots of opinions but if you are not doing big giant hole shots and slicks, it's a pretty reliable trans. I just ran through the sag in my 57, and ran it down the strip at the trifive nationals this past weekend, 261 block, 302 gmc rods, venolia pop up Pistons, Schneider cam with 492 lift, 280 duration, weiand intake, a pair of pinto carbs and Clifford headers. No problems and a ball to drive
