In general web designers and developers use Apple MacBook's... Web development is not too taxing and can be done on pretty much any build, as simple text-based editors are needed to develop HTML, CSS, PHP, JS, ASP, etc... With that said, you can go with a simple Windows PC build if you need to run Visual Studio 20XX. As long as the laptop has the ability to run core Adobe graphic's programs which are up-to-date, Creative Suite 6 at the time of OP, you will be in good shape -- if you need to design as well as develop... Which means processing power and plenty of RAM for those CS6 Adobe applications!
Best of luck!TL;DR Answer: Most web designers and developers use Apple MacBook's to develop.