You need a board that uses the LGA 775 socket type and accepts DDR3 RAM. Any board that meets those requirements will likely work with the parts you described. Also look for a Micro-ATX form factor to make sure it fits in your current case. Prices should start as low as around $40US.
If you want a faster computer, the motherboard can be a good place to start, but only as a platform that will allow you to use a newer cpu and RAM. It's unlikely to make your computer any faster on it's own, and if you get one that allows you to use your current cpu and RAM, you won't really gain anything. If you're looking for some other capability, or if the current motherboard is broken, those seem like important things to mention in the question.
Based on your comments and the image, you should be able to double your RAM without needing to purchase a new board. Just look for a single 4GB DDR3 chip (make sure you don't buy two 2GB chips). Best if the new RAM matches the timings of the old RAM... that will not only double the amount, but allow the RAM to also run faster. A quick search on NewEgg shows prices starting about $17US.
When it arrives, the new RAM will plug into the long skinny empty blue slot shown near the center of your image, directly above the CE mark.