You don’t need to really worry about linux webhosting vs. windows webhosting. That just relates to what the server’s using, but that really has no affect on you.
References :
http://www.askwebhosting.com/article/70/Linux_vs_Windows_web_Hosting_does_it_make_a_difference.html

Writing a website for Linux isn't different than Windows if you're doing straight HTML.

The main difference is what kind of technology you can run on your host. .Net, Asp.Net, VB.net is Windows, PHP, Perl, Python is Linux (usually). If you're not using any of those programming languages you don't have to alter your code in any way shape or form.

In other words, Dreamweaver is compatible with both Linux and Windows.
References :

As long as it is Perl or PHP, it should run on a Linux Host, Most linux hosts do not support ASP or JSP
References :

K Disk is an idiot. JSP definitely runs on linux, and ASP.NET works fine on Linux with Mono.

References :

All templates are compatible with both linux/windows based web hosts. And a repeated question has a repeated answer. Take a look at: http://bluehost-service.atspace.com . Their service is really great and easy to use.
References :

it does not matter, K-Disk is spreading missinformation don’t listen to him.
Make a site and it’ll run on either.
References :
http://webhosting.moneysavecenter.com/IX-WEB-HOSTING.html

Actually it’s true that many Linux hosts do not support ASP as they require additional server software. For instance http://www.onlineinstitute.com is good Linux host who supports all FTP-based web-publishing and Frontpage but not ASP, while http://www.publish247.com offers either Linux hosting without ASP, or Windows Hosting with ASP, so the best bet is to check with your Linux host about ASP and JSP if you plan to use those.

But most website design software uses FTP, which Linux supports.

References :
http://www.onlineinstitute.com
http://www.publish247.com