Hi Con
Congratulations on getting into an exhibition. The answer to your question is that "It depends"! For normal prints, it's usual to print at a resolution of 300 pixels per inch in the old imperial measure still used by printing houses. You should be able to work out from this whether your final print size is going to exceed the original size of your image (after cropping). So if you had a starting image of 3000 (h) x 4500 (w) in pixels, this would enlarge to 10 x 15 inches at 300 pixels per inch. Going larger means you will have to upscale the original image as intimated in your original request and as per Ian's response. I have done this in the past for quite large prints (40 inches on the longest side) with very good results just by using the resize facility in Photoshop Elements. As Ian suggests, better results may be possible with specific software for this but I was very happy with the results from PSE. Bear in mind also that larger prints are generally designed to be viewed from further away. Hence any impact on image quality from upscaling will be less apparent. In my experience though, the quality impact from even large upscaling is not very noticeable at close range. A few things you should do when going through the process:
1. Ensure you always work on the TIFF or an uncompressed file. Do not attempt to upscale after jpg conversion. Quality will suffer a lot more
2. In general, prints (which are referred to as images on reflected media, as opposed to images viewed on screen ie with transmitted light) have much lower dynamic range and detail in shadows will be harder to see. Also reflected media images usually look duller, and slightly darker again if framed behind glass/perspex. It's therefore usually a good idea to adjust image brightness slightly higher compared to what looks right on screen.
3. Consequent to point 2, unless your computer screen is calibrated, you will get quite unpredictable results from prints in both brightness and colour. It's critical to calibrate your monitor to get predictable results.
4. The second part to this is that the printing business should have regularly calibrated printers. These days, I think most are pretty good, even in places like BigW. However, in the past I've used a professional photographic printer (RGB digital in Brisbane). Their prices are actually better than many consumer printing houses and they courier. They will also do other print types such as inkjet in addition to standard colour photographs (Type C) prints. They will also do prints on special media such as aluminium etc. (www.rgbdigital.com.au). RGB digital recommends uploading jobs at 300 ppi and ensure the images are in sRGB colour space or the results you get back are likely to look a different colour to what you see on screen (even with a calibrated monitor). I found out the hard way once after ordering some monochrome prints that weren't in sRGB and had a nasty colour cast as a result.
Finally, before ordering in bulk, it would be a good idea to order a test print or two to check the results and compare to what you are seeing on screen.