I must say that I love reading, using and code writing for embedded systems. Most of them are designed for a specific purpose and hacking them to do other things is real fun.
If you’re looking for a cheap device to play with, then your old router probably does the job. Some routers are more hack-proof than others but in most cases you can easily upgrade the original firmware to something between openwrt, ddwrt, tomato etc.
There is a silent war going on out there between commercial and open source firmwares but that’s another post.
After some time you may want to make the next step. Well for me this is Alix!

This is not intended to replace a regular desktop pc. It’s not exactly embedded, but who cares! They consume low power, have many outputs and inputs and support mini-pci extension cards. These features depend on the board you choose of course.
The manufacturer is in Switzerland but there are resellers all around Europe so it’s relatively easy getting one. Before buying a brand new maybe you want to search in ebay for a used yet working board.
I’m about to start a project based on one of those boards. It has to do with a 24/7 eco-friendly monitoring and proccesing server. Can’t say more, wait for the project’s worklog.
PS: I’m not associated with PC Engines in any way.