HP's are pretty good. Dell's are better, in my opinion. That being said, I've never used an HP for my personal computer. I've always used Dell's. So that's what I'm used to (you could say I'm slightly biased, but hey, we all are). Acer's are pretty crappy. Asus is an excellent brand, though.
Whichever brand you get, I do NOT recommend getting a 17" laptop. It is, in my opinion, WAY too big for the ordinary user to carry around and use. It is so unportable (is that a word?) that you might as well just get a desktop (what's the point in paying more for a huge laptop that you can't carry around when you could just get a desktop?). 17 inchers are a beast to haul around. A 15 inch is more than enough. I recently purchased a netbook to carry around all the time, and left my 15 inch Dell at home for the "hardcore" computing. I like the fact that I can still carry somewhere if needed (can't do that with a desktop), but for now, it's a powerful brick that's too heavy to carry around just to check my email between classes. It is still my main computer, I just don't carry it anymore (that's what the netbook is for).
To answer your question: No, HP's are not crap. There are better computers out there, but HP is pretty standard. Yes, there are plenty of horror stories about how somebody's computer tragically failed, but that happens with every brand (it's just the nature of the beast). The situation leading up to the failure of that lady's computer is not limited to the brand. There are countless reasons why it could have quit working. Don't let that scare you away from HP.
If you want/like the HP, then go for it. If you want to compromise portability with power, get a 15 inch laptop (a 17" is no more powerful, it just eats the battery faster cause of the larger screen). If want power but don't care about portability, get a desktop. If you need super portability with super power, get a desktop with a netbook. If you do get a laptop and plan on being unplugged for more than a couple hours, make sure you get a 6-cell battery! Do NOT get a 3-cell! They last no time. I think BestBuy only sells them with 3-cell batteries (to try to keep lower prices). I would get it straight from the manufacturer if I were you.
My final recommendation: get a 15" HP laptop, treat it well, ask for help when needed (this forum is great for that!
), and it will serve you well for many years.