What kind of "grand" circuits are we talking about here? As someone who entered EE through the hobbyist approach, there isn't much I'm interested in that has me wishing I had formal EE education background. Do you want to do analog? Because there's hardly any math involved in practical applications of digital electronics.
The last 2 ideas I had were a ISA SATA card (dont ask) and attempting to build a DOCSIS modem (because issues with my shitty ISP supplied one intrigued me).
I actually tried to build a Arduino based EPROM reader for a chip I extracted from an old electronic device, but ran into some issues and am kinda discouraged because that seems like it was pretty basic.
ISA SATA card makes perfect sense to me. :) All those MFM drives are dead or dying. Protocols like SATA are implemented in hardware, and you buy an IC controller chip for the purpose. So the task with this project is to implement something that talks to the SATA controller and something that talks to the ISA bus, and bridge the two. Problem is that most SATA controllers will be designed to connect to a PCIe bus. Probably easiest to use a SATA-PATA bridge chip. Not sure how easy those are to find these days.
DOCSIS -- yeah, that's a lot of specialized knowledge to make a good one. A huge part of the complexity for that is probably board layout stuff. EMI & EMC, etc. This is a whole separate field of study on its own.
Getting that EEPROM reader working sounds like a good starter project. There's huge variation of EEPROMs though, so it would be sensible to focus on just the EEPROM you have. Who knows, your issues could have been a problem with the scavenged chip. But I2C (if your chip was I2C) is finicky and every chip seems to do it slightly differently.
