softmod of a playstation 2 memory card to run homebrew applications. link above has info on different methods of getting fmcb on a memory card and their compatibility with different models. i personally recommend just purchasing a memory card preconfigured with fmcb off amazon or aliexpress or something since i'm lazy and it's pretty cheap. follow this guide to update fmbc if your card isn't on 1.966.
homebrew application that lets you play ps2 games on your ps2 without a disc. there are a number of different devices you can put your games on and play from, some of which are discussed here. a game compatibility list can be found here. i recommend using the latest beta version which you can get here (you want the one that starts with OPNPS2LD-V.1.2.0-Beta-xxxx), a simple guide to updating OPL can be found here.
this is the method i use for playing games on my ps2. you basically put your games on a microSD card, insert it into the MX4SIO card, then plug it into one of the memory card slots. it's faster than using a usb device (quicker load times and less cutscene stutter), much simpler to set up than SMB, and compatible with my slim model. you can buy the card alone for like $10 on amazon, aliexpress, etc as well as bundled with a freemcboot card for the simplest plug and play option. information on sd card compatibility can be found here. game compatibility can be found here.
ps2 emulator for windows, mac, and linux. i recommend using the nightly build. you can find the wiki here, which has more info on how to set it up plus