PS2 Buying Guide?

Hey everyone, been wanting to buy a ps2 lately and had a few questions on what to look for:

What’s a reasonable price for a ps2, cables and controller included? I’ve seen prices on eBay and local stores (Chicago) ranging from $90-$160.

Are all ps2 models backwards compatible? I mainly want a system that can play both ps2 and ps1 games to avoid needing two separate consoles.

Is the modding process simple? Obviously I’d like to mod it to run games, but does it do so via an sd card or usb drive or memory card?

Sorry if post is low effort, but I’m completely new to buying ps consoles (have only really spent money on Nintendo consoles) and there are many games I want to experience via original hardware.