very best is internal hdd, I have a fat ps2 and the compatibility is almost flawless. no idea about how reliable are those hdd kits for slim consoles.
best primary method for slim ps2's is opl with eth (lan/network loading).
usb is a good alternative, but be warned that all ps2's have usb 1.1, thus having a slow transfer speed and videos lag.
discs aren't bad but there are many troubling factors (mainly disc brands, fragility of the media and laser life) to be a reliable method but is the most compatible, so you can run any game that have trouble running through eth or usb. I haven't ever used esr though as all the ps2's I have seen are always chipped.
you don't need a pc to setup eth, just a small mini router like this one
I have that exact mini router, you can get one (or 2, those are really cheap) from ebay or aliexpress, it does the job perfectly. I can help you with that if you want to go for that method.