You will get better image quality if you submit files for each print size you want. Just make folders on your CD for each size, or give them several disks.
Costco uses Fuji Frontier models 370 and 390, as well as Noritsu 3101 and 2901 printers. The Frontiers are essentially the same, with differences in maximum output size and printing speed. The Noritsu machines print the same sizes but have different resolutions. The Frontiers use 300 dpi, the Noritsu 3101 is 320, and the 2901 is 400.
You will run into problems if you ask the printers to do too much resizing. Noritsu printers are better at resampling images to larger sizes, but neither machine handles overly high resolutions well. You will get better results scaling your images in Photoshop, QImage, etc. and then letting the machine print.
Another point to be aware of is cropping. If you are printing images with different aspect ratios, such as the 4x6 and 11x14 you mention, you will likely be happier if you select the cropping. Otherwise, the printer will blindly crop out the center portion to fit. A more detailed workflow, including sizing parameters, is on our web site