You will have a pretty bad result with that size photo. The size at 72 ppi is enough to display on the Web, but just enough -- enlarging even to an 7x10 will result in a pretty poor quality image.
If you want too see for yourself, in the Photoshop Image/Image Size dialog, go ahead and set the dimensions to 10x7 inches (which would give you a "native" resolution of 100 ppi. Then set the ppi to 300 and check the Resample to yes, and hit OK. then in Photoshop view the image at a few sizes -- 100% to be really scared, and try viewing at the Print Size to get some perspecive. I'd say as a next step, take it to a print shop and print it out at 7x10 and see how it looks to you.
You image after the resize would be 2100x3000 pixels (a 7 1/2x10 would be slightly larger) and so you can see that an image that would print a 7x10 at best quality should hit those pixel dimensions -- in other words about 6 MP after cropping (as opposed to the <1MP image you are dealing with). Doing the resampling thing for a contest entry may give OK results, but eyeball them for yourself so that you can be your own judge.