$350 is a bit low for a new laptop, but you could find a decent refurb for that without too much hassle. Hell, you can find a lot of them! However, I think a netbook or tablet would be more appropriate.
Personally, I have a soft spot for the Acer Aspire One, partly because mine was faster than most of it’s competitors (even those costing $400–600), partly because I liked the keyboard and trackpad better, and partly because after I got rid of it, it managed to last a year in the hands of my 12-year-old cousin. Now that may not sound like long, but this boy is rough on his stuff; that netbook outlasted four cellphones!
Then there is the Toshiba Mini, a decent little machine for around $250.
@jazmina88 That surprises me. My experience is that HP gets problematic quick while Toshiba lasts forever. Reliability surveys show that that is about normal. HP is notably unreliable while Toshiba is like the Toyota of the computer world; a reputation for quality.