For digital you don't need a function generator, more like
a logic analyzer or digital pattern generator.
You might consider that many FPGA eval boards have way
more I/Os, memory depth and programmability than any
but the most expensive "big box" test equipment. The
logic levels might need buffering / shifting for some uses
but that's easy soldering practice. Many eval boards
have a "mezzanine" connector system so you could make
a "logic interface shield" without molesting the EVK at
all, and also robust PC interface software / connectivity.
Some even have low-end ADC, DAC resources which
might make for a nice little "core" for your bench.