The motherboard of your computer is the centerpiece for your Memory, CPU, and your Graphics card. Your choice of motherboard will depend upon the types of the above components you are using. A bad choice can hold your computer back. A good choice will allow for upgrades into the future. It is also important to choose the above components first (making sure that they all work together) and then finding a motherboard that will work with the components.
The first thing you should note about your motherboard is the CPU socket type. CPU are made to work with a particular type of socket. If your board does not use that socket, no amount of force will ever make the CPU and the motherboard work together and your new pc will not work.
The types of memory supported is also important. DDR2 and DDR3 are the two types found today, with DDR2 the older and slower form of the two types. The motherboard will list what types it is compatible with. It will also list the data rates of the memory that it is compatible with.
Graphics are a necessary component and some motherboards will come with on-board graphics cards while others will not. Additionally, it is important to note how many and what type of graphics cards the motherboard will support. The on board graphics will work well for simple applications and computing, however games will benefit a great deal by the addition of a graphics card. It is important to figure out what type of graphics card you will need and then make sure that the motherboard will support it.
Lastly, motherboards support certain types of USB connections and SATA connections. The new USB form is 3.0 and the new SATA interfaces (for connecting to HDDs) is 6.0Gb/s. If you are using an HDD that uses 6.0Gb/s, then you will want a motherboard that can use it at that speed, otherwise the motherboard will be limited to SATA 3.0Gb/s.
In summation, it is very important that you first understand what you need when looking at motherboards. If you are looking for a budget pc, then the older models will work fine and there are still plenty of older components on the market. If you are looking for something with upgradeable potential, then there are lots of good choices too.