One common (and sometimes frustrating) response you'll get is, "Play something you like!" That isn't always helpful to someone who is still trying to figure out what games make for good speedruns, but that's also part of the point - ANYTHING can be speedrun! Think of games like the Tetris Attack/Panel de Pon series - RNG defines nearly the entire run, and yet you have players like Bbforky and CardsoftheHeart who get terrific times through endurance, stellar play, and patience.
At its core, speedrunning is just playing with the intention of going fast. Advanced skips, glitches, and WRs are nice, but they're not the sole focus of the hobby. If you find a game you like, beat it, then go back and think about how it can be done faster, and do it, you're speedrunning.
That being said, if you're on a laptop, then surely you know by now that the Steam store is full of buried treasures. Tons and tons of 2D platformers, often available on sale for very cheap. Here's a list that comes to mind (it's going to be a little self-serving, because it includes my main speedgame):
VVVVVV INK Xeodrifter Oniken Super Meat Boy Broforce Out There Somewhere Camera Obscura LIMBO BEEP Oddworld series
They also have tons of classic Sega Genesis/Mega Drive games available. you'll have to check with each community to see if the steam version is allowed or not, but I have to believe a low-powered laptop could handle them just fine.
Hope that gives you a place to start! If not, then just go back to the front page of this site. Look at the recently submitted runs, just scroll down, and click one at random and watch it. You'll start to see some common themes that apply to all games from a speed standpoint!
OMG GET REKT DELN YOU IDIOT BOY
Getting on topic, though. Platformers are the ultimate speed genre.
Oh, I didn't mean to diss Deln. It's a good point, truthfully! He actually submitted that while I was typing my dissertation, so I didn't even see his post! :D Now I feel bad.
Also don't forget that you can play console games too with a crappy laptop. If it's not too bad then it should handle for example an SNES emulator quite well, which has some great games for speedrunning. Just check them on the site here. I could recommend Super Mario World 11 exit. It's easy to learn and even if you do bad, you will improve quickly. Also lots of players have run this, so it's kind of fun to start in the leaderboard from the bottom and slowly move upwards. :)
Remember you don't need to get god times to be a speedrunner. Just make sure you improve even if it's slowly, it doesn't matter. You will get WRs if you find some games which are absolutely yours, but until then just do some runs and have fun.
I Wanna Be The ORE TUEEEEE!!! is a very short game should be easy to get a place on the leaderboards and then you can work yourself up. Perfect for beginners
If you have a Wii I reccomend Mario and Sonic at the Olympic Games. Its ez to run and if you are good at the controls (or bad at times :P ) you can achieve a good time.
