I'd definitely go the FPGA route initially, it has software like advantages such as being able to reprogram stuff without having to tear it all up and do it all over. It also elegantly avoids having to build up soldering skills (which is a bit of a pain with SMD) Once you get the hang of that some simple CMOS circuits hole-through on a breadboard would be a gateway drug to building stuff for real. If you want another in-between step I'd go for a kit of some sort, something that you want to have anyway but would rather build yourself, there are quite a few producers of such kits and they range in complexity from 'blinking LED' to 'build your own glass teletype' and everything in between (and even more complex).

Compared to software it is a costly hobby though, and it also occupies more space beyond just a laptop. And it can be quite messy.