First of all, make sure that what you need is a laptop. Because for the most part, what you see is what you get with them. Compared to a desktop PC, they're incredibly hard to upgrade or even fix. Desktop PC components are much easier to find compared to laptop parts.
That being said, if you want something that doesn't cost a ton of money but still packs a punch, I'd go with an IBM Thinkpad. I don't like HP, especially since the merger with Compaq. I would resonate what others have said - that processor isn't going to do it for you. 512MB of RAM should be fine for any practical applications. I'd just definitely look into getting a decent processor, you'll be kicking yourself later if you don't.
Really, if I were going to get a laptop, I'd be looking into portability and wireless capabilities. I'd go for something around 12 inches just because small laptops rock the house
