Games you like are always a good place to start. If you don't want to be spending money then pick a genre you like and maybe find some flash games you could run? Newgrounds, Armor Games and Kongregate are always a good places to start with for things like that.
We can't pick games for you to run because we aren't you. We have different tastes than you, we don't know what you like, dislike etc.
Think for a while. Think of the very first game you had so much fun with that you always wanted to play. Choose that one and then advance if you feel like playing another one of those games.
I wouldn't even make that big of a deal out of it and think back to the first game you liked so much. Just take a look at games that you really enjoy lately. That's what I did with Grandia II. I came across it, I enjoyed it and I started speedrunning it.
For me the moment I think to much about possible games I don't feel comfy with it and don't wanna start playing anything from the beginning.
play games you like and if you want to play them differently then maybe look into speedrunning them. If you start speedrunning a game or when it becomes more of a hassle then fun for you, it may be a good sign to try another game or change how you are doing it.
Most important thing is always have fun with it. <3