When those came out, you were probably running a Pentium 3 with 512 MB of DDR2-800 and had an 80 GB hard drive. If you're still running that as your PC, be careful, because modern desktop operating systems and programs are also considerably heavier. Stick with Netscape for browsing the web, though there's a new browser called Firefox in version 0.9. Napster recently shut down, but yes, your old Tomato firmware should be nice and snappy while using Limewire over your DSL modem, FreshTomato, with all the options built in, might not fit.
This will, indeed, run best and be enable the most features when using a router that has a comparatively generous 128 MB of Flash, 64 kB of NVRAM, and 128/256 MB of DRAM. Those are no longer opulent or excessive stats. Wifi AC is out, treat yourself to something with MIMO antennas, a dual-core 1+ GHz ARM processor to run all the neat plugins you might want to use, and USB3 storage. Even with that higher power, switching power supplies have improved dramatically in the past few decades, both the router and the power brick will probably not be as hot as on that old router at the same time as they're doing more and doing it faster.
For example, the image I used on my router was 27Mb, but the smaller "min" image for the relatively old RT-N12 was only 3.6Mb.