Custom router firmwares are different that linux distro's as in custom firmwares are stripped down linux versions. I would advise installing linux on a PC just to get an idea on Linux.
Disto's which are nice to start with are UBUNTU, CentOS (Redhat) and my favorite but more hardcore Gentoo.
If you would like to go custom on firmwares I would advise OLEG firmwares. They are based on the original ASUS firmwares with added stability and application support. I'm not 100% sure OLEG has a firmware for your router.
I'm using OLEG firmwares with great success.
Routers are crappy nowadays since all router builders like Linksys are reducing RAM to make more money and sell inexpensive product. I myself have 2 ASUS wl500g premium which I had to debug with a soldering iron to bring up the performance by 10db-15db and then even had to add 2 10db antennas to get a satisfactory WDS link. ASUS routers have good potential to be good routers due to RAM, CPU and support from communities like this.
Custom firmware has given my router more possibilities and options and to me it's a little linux system. I hope your quest will lead you to a good working system.