When doing a large print the main thing you want to be concerned with is how many pixels are in a file. The higher the PPI (pixels per inch) in a file the better quality the print will be. You will be hard pressed to get good quality prints the size of 24" x 24" with a pocket sized camera. The optimal amount of pixels desired for a 24" x 24" print is 7200 x 7200. Usually with a point and shoot you can go up to a 11" x 14" print max before the image starts to become pixelated. (Pixelated means you will have a blurred or unclear image.) For an 11" x 14" the optimal amount of pixels desired would be 3300 x 4200.
I personally have only ever used Canon cameras. If you have your heart set on only purchasing a pocket sized camera, I would suggest the Canon PowerShot S95. (Runs anywhere beteen $350-$500, depending where you purchase it.)The camera is about the size of a deck of cards and fits into a shirt pocket, making it easy to take with you. However if you want something that is going to be used for sports or other action photography don't buy this camera. It should also be noted that there is no viewfinder on this model. If you can't compose a photo without looking into a viewfinder, then this camera is not for you either. The S95 does take decent photos though and also allows you to shoot video.
I use Nations Photo Lab. They do canvas gallery wrapped prints. A 3/4" - 11 " x 14" costs $70 to get done. 1 - 3/4' - 11" x 14" is $72 and a 2 - 1/2" - 11" x 14" goes for $95. It would be $130, $135 and $170 for the 24" x 24' sizes. Besides PPI, correct exposure will also determine the quality print you received in the final product.
In my opinion if you purchase the pocket size camera, stick to getting 11" x14" prints made, put them in 16" x 20' mats and frame. They will look classy in a place.
