Microsoft recommend 1 GB, but they always under-recommend, 'cos they'd rather you spent your money with them than on hardware. Frankly, I wouldn't bother with less than 2 GB, especially as modern RAM is so cheap.
Inspiron 1525 covers a whole range of specs, so impossible to say if the one you have in mind is any good. Personally, I hate laptops, but if I had to have one, I'd be looking for a 17" rather than a 15". Acer do some well specced machines.