First, the previous posts provide valuable information. I thought I would add a few other considerations.
When asked about what computer to buy, my first question is "What do you want the computer to do?".
If your need is mostly for email and the Internet, then I usually recommend that you buy a standard (meaning low cost) machine. The most basic computer is equipped to handle email and Internet.
For a basic machine, the add-ons that I recommend are:
1. Get plenty of RAM (Random Access Memory). This is the dynamic memory that running programs use and the more the better. For a new computer, I would like to see at least 512 MB. This can be easily added on to an existing machine for a small additional charge.
2. If possible get the Windows XP Home Edition CD with the computer. Most new systems do not provide the CD, but you can often get one for a small price ($10 in the case of Dell). It will pay off by easing system repairs.
If you want to work with image files or video, then you will need lots of RAM (at least 1 GB) and a very good display adapter card with its own built in memory. For this use, I would suggest you speak with a knowledgeable computer person, because choosing the right components will make a lot of difference. This type of application would benefit from having a machine custom built for you.
I'm certainly not opposed to buying your machine locally, or having it custom built. But you will pay more for this when compared to prices for a Dell, Gateway or Compaq computer purchased online (or via 1-800 phone line). Again, if you need a basic machine, it should only cost about $400 including shipping.
http://www.dell.com/tvConsider this one: Dell Dimension B110 - $299 (basic cost).
Add the additional memory (512 MB Total) and the WinXP Home Edition CD (to ease system repair, if needed) the price is: $359. Add the shipping costs and you're at about $400.
You mentioned that you didn't need a new monitor and this one does come with a monitor. If you call the Dell people, you can ask to have the monitor removed and the cost deducted (probably around $40). The number is on the page linked above: 1-877-887-3355.
I used the Dell in my example just because I'm most familiar with them. I have purchased or helped with the purchase of many systems for my clients and have been very happy with the Dell. My biggest reason for recommending the Dell is because they have a good support Website and every computer will need technical support. But the HP, Gateway and Compaq (now part of HP) sites are also good. I know there are some who feel strongly about one machine versus another, but the machines are not all that different. The main things I'm concerned with are the warranty for at least the first 90-days (this is when most problems are found...if it works beyond that time it will most likely run well for years, a truism for most electronics). And the support site, as mentioned above.
About software. I generally recommend that you purchase software that you want separately from the computer (not pre-installed at the factory) so that you will get the retail version of the software. Having the retail version will usually help with support issues from the software maker. It also eases reinstall problems. And it is often less expensive. For example, take the MS Office software suite (MS Word, MS Excel, MS Powerpoint and MS Outlook (email program). Dell charges $149 to pre-install the software. You can usually purchase the Student/Teacher version of Office at Best Buy or Wal-Mart for about $130 (and I've seen it as low as $100). You have the exact same programs and the retail CD for less money. To qualify to purchase the Student/Teacher version, you just need to either be a teacher or have a student in your household (kids, grandkids, neighbors kids, etc.).
You new machine will likely come with lots of software that you don't want or need (AOL, MSN Explorer, various ISP (Internet Service Provider) offers, etc.). Whatever you're not using and will not use, you can uninstall via the Control Panel, Add-Remove program utility. This will save storage space and simplify your machine.
Finally about Internet speed. This is mostly a function of the type of Internet connection you have, not the computer itself. A broadband connection like DSL or Cable is going to be much faster than a dial-up account (even if one buys the accelerated version). This is true of your current Gateway 2000 or a new mega dollar machine. So if Internet speed is important to you, consider the Internet connection type first. All new computers will come with the Ethernet adapter card built in so they will be able to accept broadband connections.
I hope something here will be helpful.
Dwight