I assume that a Linux platform website doesn't mean I need Linux to program it
Not at all.
Linux/Unix powers about 80% of the web. (simply because its better suited to it and arguably more secure) It has no bearing on windows users and you dont need a linux system to develop on at all.
If you are going to be doing more advanced things like PHP or SQL stuff its often handy to set up an apache server (its free) for "localhost" or LAN only on your machine so you can develop and test your site before uploading the changes (Apache Server runs on windows or linux).
However, if you are just going for simple stuff like HTML+CSS, Flash etc.. you dont need to do that, you just need an html editor of some sort, paint package and an FTP program. You also need a browser to test with and for this it is best to mostly use FireFox as it is stricter and you end up with more compatable universal-standard code.
I strongly reccommend learning PHP too, its real easy to learn and allows you to do all the stuff you wish you could do in html (only downside is you *realistically* need a local dev server).
The only thing you cant do (AFAIK) with a lin/unix system is use MS only server-side stuff like ASP. However you can use all the just-as-good alternatives like PHP, perl etc.
The only real reason its cheaper is because there is no licencing costs to the hoster.
btw, if you are going to use netpivotal, use their .com domain when accessing their services (it doesnt have all the annoying certificate messages all the time!) but sign up to .co.uk (if in UK) because it *might* affect where you are physically hosted.