I have an old laptop too (40GB hard drive, originally 256 MB RAM until updated because it was very painfully slow). idk really about the new laptop. Your best bet is avoiding the main PC shops like PC World and instead visiting proper computer shops, the type where they have a standard PC which you can buy but also upgrade and downgrade as you wish. Dell is a good example, as Sky suggests, but I can't suggest any other names since I live in the UK and idk if they would ship PCs abroad and even if they did, if they would be compatible with foreign goods.

Why not get a bigger screen? Unless space is limited, a 17-inch one would be best. You could also buy yourself an external hard drive to give yourself extra space, that's what I did. I wouldn't recommend Toshiba for the laptop though, unless they've improved over time. My laptop is Toshiba, is 4 yrs old, and has never worked particularly well and I've never felt at comfortable with it as I did with the old desktop which broke.