That's the $64,000,000 question! It depends entirely on what you want to do with your Linux installation. If you want a full GUI desktop install, that's going to take up 2-4GB on its own. Because there's so much free software available with a typical Linux distribution, it's fairly easy to install 10GB of software - before you've even started to put any data on the system. Incidentally, you need at least 2 partitions for every Linux install - one for the swap file (virtual memory). In your case, that partition should probably be around 256MB-400MB.
Linux is typically not so demanding on a system as Windows, but it does like memory - RAM and hard drive space.