Now, I'm no hardware expert, so anyone feel free to add things to this but, here goes.
Price: motherboards over $100 are generally considered higher end. Most probably, you can get a perfectly fine one for less.
Brand: There are several big brand names that are know both for reliability and quality products: Asus, MSI, Soyo(expensive) just to name a few.
Intel/AMD: Now, I am bias because I have always used AMD. Intel will probably be a better choice for daily buisness work, but AMD is better for gaming, and is also fine for the daily routine. AMD tends to be cheaper also when it comes to processors that arent "cutting edge". Now, I think you might be confused with something here.. Motherboard DO NOT come with a processor. It must be bought separately, along with a heatsink(normally included) and fan. I would suggest a retail AMD Barton 2700-2800+(Im currently running the 2800) but it is certainly up to you.
Installation: Installing a motherboard is a fairly easy task, but it is also a risky one. If you have no idea what you are doing, its generally not a good idea to tackle this job. The motherboard comes with plastic spacers to offset if from the case on installation, thereby not letting the metal complete the circuit and fry the whole board. Granted, it is pretty hard to mess this up, but it has been known to happen. Moreso than just the board installation, the processor and heatsink can also lead to major damage. If the heatsink is not installed properly(plastic can't be touching it off the CPU) it can again case a very bad day.
expansion: almost any motherboard today provides for decent expansion. If you mean RAM slots, then almost all have three nowadays. PCI/AGP slots are also pretty common. Other features such as RAID, etc. wil cost you more, but if it's something you need then you might want to look into it. Also, you can commonly find motherboard with onboard sound, video, and NIC. This is a good space saver if you are not concered with having the utmost quality in these areas.
Choosing: When choosing a motherboard, there are a few important things you want to look for. First, make sure it supports the processor you want to buy. Either Intel or AMD. And make sure that it can support the clockspeed of that CPU(it is always clearly labled on the box). Next, the front side bus. The motherboard must be of the same FSB as the processor, and the RAM as well if you want to take full advantage of the speed. (Barton 2800+ runs at a 333 FSB, Itel is always higher in recent models). Finally, look for the features that are important to you.
RAM: If you wanted to just keep the system you have, it is possible to buy higher density RAM. For instance, you probably have two sticks of 256mb RAM currently. You can get anywhere from that to 1ghz or even 2ghz in a single chip! So, RAM slots should not be an issue.
CPU: Assuming you bought a compatable board, it is possible to take the CPU out of you existing Compaq and put it in a new one. However, since it seems that you have not had much experience in the area, I don't suggest you try this.
Well, hope I didn't leave anything out. Good luck on you purchase!
Edit: If you wanted to order offline, I suggest www.newegg.com I bought my entire computer off the site, and may other things since. Great site. Also, if you get it from there, I can help you directly find the one that you want/need.