ME1 is great. It gets a lot of shit for its inventory management and vehicle controls, but in truth I like it a lot more than ME2. The actual combat is more RPG based. It's still a shooter, but the damage you do and whether you hit or not is based on your stats. This is really only a problem at the beginning of the game, but the combat gets a lot better once you level up.
ME2 took a lot of what made ME1 a good RPG away and made it more of a simple third person cover shooter. Not a bad game by any means, but I much prefer 1 over 2, but I can understand why people might dislike 1.
Anyway, the gist of all of this, is that no, you don't NEED ME1 to enjoy ME2 and eventually ME3, but I do recommend trying it. You can get it pretty cheap ($10-$15 for PC). I can't speak to how well it'll run on your computer, but if you can spare the change, it's worth it.
Also, I'd like to mention that ME1 is actually fairly short if you stick to the main quest. Most of the side quests aren't worth it, except for a select few. Stick to the main quest, and ME1 is a ~20 hour game. ME2 is probably around 30-40 hours.