I wouldn't go with Acer nor HP. Acer(Lenovo,Packard Bell) is one hell of crap quality, HP known for bad design of cooling and overheats.
I suggest you go with Samsung, Toshiba. Maybe Asus, they used to be awesome, defective too much now.
Runescape and Youtube Vids really can run on any laptop nowadays. The quality of the game/videos is more dependent on your internet. I have a great laptop but absolutely terrible internet so my Runescape/Youtube experience sucks. Having an Alienware M18x wouldn't change that fact.
That being said, I'd go ahead and say the HP since it's cheaper and since you don't seem like you're going to be using the laptop for anything really demanding. If you are still looking at other options though, I'd look into a brand like Asus. Acer and HP aren't exactly the most reliable laptop brands out there.