If its a mild 350; grab a saginaw 3 or 4 speed. Muncies and the hot rod T10s go for close to a grand and unless you know what you're looking at, you might end up with a box of junk. You can still get a box of junk from a saginaw, but its a much cheaper box of junk.
Do yourself a favor; don't build a rat rod; fix it right, use quality materials, some ingenuity and a lot of elbow grease. The main thing with your first hotrod is to actually get it on the road under its own go and whoa power, and where you dont let the smoke out. Once you can fix all of its systems, and you can afford a second car, take it off the road and get crazy with it if you want.
If you need saginaw hard parts (gears forks etc), you'll have to buy good quality used ones (I'll hook you up with some people if you get to that point). If you need an overhaul kit, PM me and I'll help a brother out.
Ask questions and listen to the guys who worked with this stuff when it was new. Find a Hayes or Chiltons or Motors manual that includes 1965. I like the old Motors ones best; because it covers more makes and models; this way if you get a 69 sag; it'll be covered. You want something with a 2.5 - 2.8 1st gear ratio.