Let me suggest a structured approach. Here is a list of components you should be aware of, and do some research on separately to know what is currently available on the market and how fast it is and what you need.
CPU
RAM
Hard Drive
Video Card
Screen
Operating System
The CPU isn't really that important because most modern CPU's will do a great job. Get an Intel Core 2 Duo or an AMD processor, and check out benchmarks to see how they compare in various applications:
Some modern mobile CPU benchmarks here:
http://www.tomshardware.com/charts/mobile-cpu-charts/Divx-6.6.1,469.html
A much larger list of mobile CPU's that includes old models for comparison purposes as well:
http://www.notebookcheck.net/Mobile-Processors-Benchmarklist.2436.0.html
Next, consider the RAM. If you get Windows XP I would recommend about 2 Gigs of RAM. If Windows Vista or the upcoming Windows 7, I would recommend at least 4 Gigs of RAM. What kind of RAM you get really makes absolutely no performance difference, at most it is very very slight and really doesn't matter, what matters is the amount in Gigabytes. If you don't have enough Gigs of RAM, your computer starts using your hard drive as RAM, and that is extremely slow and will make your entire system crawl so make sure you have at least the amount I mentioned above so that won't happen.
Next, the hard drive. This is probably the single most important component you will choose in terms of how fast your computer will feel. A CPU is rarely utilized except in CPU-intensive applications like flash games, games, video rendering, etc. Typical stuff like browsing and email and watching videos and music (unless it is HD videos) won't use much CPU, and most modern CPU's will take care of that stuff very quickly. The major hurdle is the hard drive because every single program you open will have to be loaded from the hard drive no matter what it is. And no matter how fast your CPU is, if your hard drive is slow (or you don't have enough RAM as mentioned above), your computer will feel very slow and everything will take forever to open up and load.
I would strongly urge the hard drive to be your #1 consideration and I would advise sacrificing the CPU a little if it means you can afford a faster hard drive. The size of the hard drive in Gigabytes is only important in terms of how much stuff you plan to put on your computer, but the speed is what makes everything feel faster or slower while using the computer. There is no number you can look at that will indicate your hard drive's speed like there is Ghz for CPU's (although with current focus on dual-core and quad-core and architectural improvements, the Ghz means less and less for CPU's too). For hard drives (and for CPU's for that matter) you should go straight to benchmarks to see how fast they are.
Here are benchmarks for mobile hard drives:
http://www.tomshardware.com/charts/2009-2.5-mobile-hard-drive-charts/benchmarks,53.html
You care about the Read Throughput and Write Throughput mostly.
For a good indicator of realiability and customer satisfaction check out newegg.com and see mobile hard drives and sort them by rating to see which are the highest rated by customers.
You are of course not limited to buy hard drives on the above benchmark list, but whatever laptop you buy, just find out what hard drive it has (the exact manufacturer and model number) and look that up in a search engine with the word benchmarks next to it to see how it compares to others. The faster the better. If you are shopping in a real physical store, you can find out what hard drive the computer has by going to Device Manager (ask store employee how to access that in Windows).
As for video cards (graphics card) also look at benchmarks, but unless you want to play the latest games I'd recommend being conservative with this component and putting more of your budget into the hard drive, the RAM, and the CPU. Laptops are not good for games in general and will get very expensive very quick if you get powerful video card, so for a $600 budget I would recommend a lower-end discreet video card (one that is not built into the motherboard), or even one that is built in to the motherboard.
Video Card benchmarks:
http://www.notebookcheck.net/Mobile-Graphics-Cards-Benchmark-List.844.0.html
I would recommend getting a sense of what kinds of CPU's you are cosidering and making a list, same for hard drives, and video cards. Then finding a laptop that has the components that you are considering in your list, or others that are comparably fast by looking them up in a search engine with the word benchmarks next to them.
A Core 2 Duo of about 1.8 Ghz or above is usually a safe choice for CPU's. Hard drives that are over 70 MB/s Average Read Throughput are going to feel pretty fast. 4 GB or more RAM is also a safe amount for almost any kind of workload, and I wouldn't get any less for Windows Vista or Windows 7 - RAM is cheap nowadays anyway. Also an alternative to a Hard Drive is a Flash drive which, like the Intel flash drive brands are much faster than any spinning hard drive, but they are way too expensive for most people right now and will only become a good option in about 2-3 years at the way prices are falling now.
Good luck! All this info can be overwhelming if you're new to these components but some thorough research and reading about these things will really help you understand what you are getting. I would recommend going to a store like Best Buy and at least playing around with their laptops to see how they feel. Some little things can make a big difference - how the mouse pad behaves, how the keyboard is layed out and feels, the existence of volume buttons, etc. Hope this helps!
