Resolution isn't so important for that - what you'll want to do is reduce the color spectrum when just a few colors are involved (IE make sure all the Pioneer greens and yellows are constant colors, not different shades of them) and then convert it to a vector image, which can be resized infinitely without any quality loss or pixelation. Pretty much all graphic design images end up in a vector format for this reason. It doesn't work when there are photos or fine detail and color difference though. Basically how they work is that instead of the computer mapping a color to each individual pixel as in a normal JPG or BMP, the image is reduced to basic geometry, and colors are basically determined by lines and boundaries. So if you had a white circle in a black square, instead of having to assign a color to each pixel, the computer just sees the boundaries of the square and fills everything inside with black, and then overlays the white circle and fills it in. And since those shapes are determined proportionally to the overall image size instead of a pixel count, they can be scaled up or down without any quality loss whatsoever - theoretically you could make a sign the size of a sheet of plywood from a little 1" X 2" scanned image if it's done right. When normal bit-mapped images are scaled up, the computer has to generate new information from nowhere, going by closest colors and patterns etc which is why enlarged photos get a "blocky" appearance after a point.
Free online vector conversion website