Neal, in the Build your own CNC book they use 1/8" all angle so thickness is OK but I am not sure 3/4" is wide enough to mount the bearings on. The book uses 1" or 1 !/4" ally.
As for router they say you can use any DIY type router but the problem with them is speed control. Even variable speed on it's slowest is to much for acrylic & melts it rather than cuts it. The guy I know who has already built one of the book machines tried everything & eventually had to buy a super pid to control the speed.