You've gotten lots of good advice, Marci Anna, but I'm going to pile on a little more--you get to decide its worth.
If you're not going to use your weather computer for much else, it can be a fairly low-end setup. Unless you're used to building your own computers, buying one without a monitor is the best route to go, and it will actually be cheaper. I'm very comfortable with Newegg, a vendor that has already been recommended in this thread. They are very reliable, ship fast, and their prices usually can't be beat. I usually look there first for computers and related items. For instance, here is a very low-end HP dual-core Pentium 3.0 GHz processor with a 160 GB (adequate for a weather PC), but no serial port (do you need one?):
http://www.newegg.com/Product/Product.aspx?Item=N82E16883147482 Less than $300 gets you a recertified and/or generally underpowered machine. My current primary weather computer is a Newegg purchased low-end Lenovo with which I'm very happy. Here's a similar one to mine for $380, again without a serial port:
http://www.newegg.com/Product/Product.aspx?Item=N82E16883108456 Here is an Acer that has a single-core 3.2 GHz CPU but with a serial port:
http://www.newegg.com/Product/Product.aspx?Item=N82E16883103374 for $300. All of these also have free 3-day shipping.
KVM switches come in many different configurations and with different capabilities. I've used them for many years--I have old functional PS2 VGA dual and quad KVM's without audio that I started with that are now just sitting in my junk closet. I've lately moved to IOGear KVM's with DVI, audio, and USB mouse/keyboard because they generally will allow you to boot a computer that isn't switched to the monitor, keyboard, mouse, and audio. They're designed to remember all of your monitor's capabilities and then trick the computer into booting up with the appropriate video settings.
Adding a second hard drive, internal or external, is a good way to provide backup for your data and your computer. Windows 7 comes with decent backup capabilities that can take advantage of an additional HDD(hard disk drive). A 3.5" form-factor 1 to 1.5 TB USB-attached external HDD is fairly inexpensive these days. Other solutions would be using an off-site backup such as Carbonite which my sister uses:
http://www.carbonite.com/en/default or network attached storage with redundant RAID-configured HDD's. RAID storage provides redundant data backup so if a backup drive fails it can be swapped out with a new one yet no data will be lost. For $60 a year, Carbonite is probably the one of the most cost effective solutions, but restoring data over the internet rather than from a local HDD could be tedious.
Uninterruptable Power Supplies(UPS's) are also an essential ingredient of a reliable weather computer unless you go with a netbook or laptop because they already have a built-in backup battery. Our power is generally very reliable here in NE, particularly if you have an underground feed like I do. What WILL get you, though, is that temporary loss of power for a second or two while the grid recovers from an 'event'. Other than planned outages such as for transmission equipment upgrades I've only experienced one extended outage in the past 20 years, and that resulted from the October 1997 snowstorm. You need basic battery backup, but probably not much more. All of my computers are on UPS's, and I do get tired of trotting off to Interstate Battery for replacement cells for them. The cells generally last 3-4 yrs.
Have fun shopping!
