Moderately easy computer circuit to build?
The idea of building your own plugin board for a PC died about 20 years ago when mainstream motherboards stopped supporting the ISA bus. PCI, let alone PCI-E, is simply far too fast to be used as a starter project. Likewise, modern ICs such as A/D converters are increasingly supplied only in very small packages.

If you really want to roll your own circuits and communicate with your PC, I'd advise getting a USB to parallel converter, and get some older parts such as an A/D converter in a DIP package. The USB line will be able to communicate more than fast enough for your purposes. 

Alternatively, use the USB interface to drive LEDs, as has been suggested. You seem to have made an LED project of some sort, but revisiting it with a USB link will be an excellent transition project. After all, you know how to drive the LEDs, and any problems you have you can be fairly sure it's the link that needs fixing (hardware or software). This will reduce the frustration factor when it doesn't work the first time. Unless you're an adrenaline junkie (and some are) it's best to increment your skills one skill at a time.