If you're a beginner, you definitely don't need to dish out the cash for the most expensive most powerful laptop. A php/apache server is not very demanding when developing and you're the only one sending requests. You don't need to build a server, just have a simple development machine.
I would also say that having the most high-def screen is unimportant with web design as you will likely be saving somewhat compressed images in order to serve files faster. Don't just test your site in your native resolution. Be sure to look at it in various resolutions. 1024x768 is still used in many schools and offices.
Also (as others have said), be sure to test it in all major browsers in order to make sure it works with everything. You'll likely be running multiple browsers with multiple tabs open simultaneously. Remember, code for Chrome/Firefox, fix for IE. I completely agree with buying additional RAM, running dual displays, and virtualizing Windows for IE. Also, be sure to virtualize IE 7, 8, and 9 (not just the most current IE version because they all act differently...). If you have an old windows machine laying around, you could always just test your sites on it for IE, or VPN into it to test.
I work at a company that does web design and I still have an older dell machine that I run Ubuntu 12.04, a Ruby on Rails server, and two monitors with. It gets the job done just fine and only has 1.5GB RAM. When you get more into web design you'll realize you wish you had three monitors even.