To help you the best, let us know what the actual pixel size of the image is. (i.e. 1600x1200, 2048x1536, etc.) You say that it works at 4x6, so we have been using that as a guide. Knowing the actual aspect ratio may offer even more options.
I was suggesting that you print it on an 8x10 but the actual size will be more like 6.67x10. It all comes down to how much you want to spend. At most printing places, the price goes up sharply once you get past 8x10 because the next standard print size is larger than a standard 8.5x11 paper size. That often requires a much more expensive printer. It all depends on the place though. You are likely to get a better deal with a larger organization like
Walmart, Target, or one of the online places. I believe that Walmart uses Fuji processing and Target uses Kodak. I would not pay more than $10 for the 8x12, but some places may charge $30 plus.
The 6.67x10 will likely be printed on 8x10 paper and the 8x12 will likely be printed on 11x14 paper, so look at those prices. Some places will want to charge you extra to trim off the unused area of the print. I can see why they would want to charge if it is 100 prints, but if it is only one or two, I would not be happy if they charged me for that service. Check first before you order the print. You can trim it yourself, but if you mess up, you have to go buy another print. Another option is to ask for it centered on the paper with no trimming, if you are going to have it matted and use a larger frame.
No matter what size you decide, I personally think that framed pictures look better when you use a larger frame and matting. Professional framers will have a large selection of matting colors, but this is one of those things that you can do yourself cheaper if you have the skill. The lines are not that difficult, it is the corners that get me. My Walmart sells inexpensive uncut matting, but only in off white.
Not to complicate things any further, but you can always add your own digital matting in your image editor. Many editors have a built in function to do all of this for you, so check for that first. It may be called a border in the program. If not, you start with a new blank image that is somewhat larger than your original and that has the same aspect ratio of the frame you want to use. Set the background color to the color you want for the matting and then paste your image in the center. To add even more effect, you can add a small border (5-10 pixels) around the actual image that is a slightly different color than the matting color. This does not look as nice as real matting, but is free.
Good luck!
Kevin