Then you don't need amazing specs. You don't even need multi-cores like the i3, i5, or i7.
I'd say, in your situation, opt for a bigger hard drive (500GB+) to store loads of files and at least 2GB memory (RAM). You can get mad-sized memory, like 6GB, 8GB, or even 24GB (in PCs!), but I don't see why you'd need that. You also wouldn't need a dedicated graphics card - just shared graphics would do. You also don't necessarily need 64-bit Windows, if you get a laptop with less than 3.25GB memory.
How about this, if you don't mind used goods?
http://www.amazon.co.uk/dp/B002Q8HMD2/?tag=brite-21 I love Toshibas. 500GB hard drive, 4GB RAM, 2 processor cores for doing tasks simultaniously...
If the "battery is not guaranteed", which is normal on a used laptop, you'd just keep it plugged into the mains.
Or buy a new battery in the future. We'd all help you out one finding the correct one when the time came. eBay has good cheap ones.