If you intend to test ICs with various supply voltages, then you definitely need either DACs or some other circuits supplying needed voltages to tested ICs.
Also, in such a case you'll need suitable level shifters to connect your IC outputs to your uC.
The best you can do is to decide to use ICs supplied with just one voltage, say 5V.
This would simplify your design greatly.
Once your HW is ready you'll need to define test vectors for your DUTs and response signatures your uC will compare against real responses from tested ICs.
I saw once a design of such tester for TTL devices.
I guess it was published by Steve Ciarcia in the Byte magazine around middle 80's.
Perhaps there are pdfs still available...
Besides, if you decide to test just TTLs, the design is not this hard
All you need is ample memory to store test vectors, and of course a simple 8-bit uC with sufficient number of I/O pins.