If you are unsure what type of web hosting you need, go with Linux hosting. There is nothing initially wrong with Windows web hosting however, it is used for very niche services that you would not be able to run on a Linux server.
If you need any of these things, then you might want to shop for Windows web hosting:
- Remote Desktop
- MS Access
Compare shopping differences between Windows web hosting and Linux web hosting to buying a couch. Windows hosting would be the couch that fits in a very specific spot where Linux web hosting would be more like buying a series of bean bag chairs that you could put anywhere in the living room.
There are also very specific tools you can only use with Windows hosting. Take a look at hosting control panels. Where Linux web hosting accounts usually come with cPanel (or a combination of cPanel/WHM), Windows hosting often comes with Plesk.
Which option is more secure? Windows and Linux server can both be as secure as you make them. I would not say one or the other lose that fight based on just being a Windows server or a Linux server.
The operating system you are currently using does not matter. You could be running OSX, Linux, Windows or anything else and you can use whatever web hosting account type you want.
The fact you need to remember is in web hosting, your Windows versus Linux battle is opposite of what it is on your desktop. Where Linux is about 1% of desktop PCs – Windows probably covers the other 99%. In web hosting, Linux is king with 99% of the market and Windows is the 1%.
My best advice to you would be to figure out the tools you want to use to run your website and then see if your hosting plan you have in mind supports it.