So I've had a Dell Inspiron 1545 (
http://www.amazon.com/Dell-Inspiron-.../dp/B002PY7OKI) for about 4 years now, and I've actually really liked it in terms of playing ffr/sm. It's a fairly inexpensive laptop, so it only has 4gb of ram and a 250gb hdd. This actually works well for me and might for you too, since I use it for very simple things like school work and general internet browsing, as well as ffr and sm. The battery life is fine, but I opted for a better battery when picking out upgrades and whatnot.
As for ffr and sm, I can't stress enough how happy I've been with it. For the first 3 years or so that I've had this, I've played both ffr and sm a TON. And not just easy peasy stuff, I was playing a lot of dumps and stuff where the keys are really taking a beating. Speaking of the keys, I've had the same set-up for maybe 2 years now, where I keep my wrists elevated and it works out great. Those four keys are a little worn down, yeah, but none of them have stopped working or anything.
So in short, I don't think this laptop could've been much better (for me) for playing sm and ffr to my heart's content. Also, I don't have many other gaming needs, or else this laptop would be less than ideal. I can play stuff like terraria, and maybe some other simple steam games, but not much beyond that. Hope this helps.
also: I've never had any shaking display type issues like what justin was describing