Adobe Photoshop has been the gold standard for photo editing and manipulation, with a price to match.
This link looks at the various Photoshop and Photoshop Elements offerings based on the tasks you need to perform.
Adobe is now providing their products as an on-line subscription (Creative Cloud). You pay a small amount per month, and can download and install the latest Adobe applications on your local computer.
While Adobe offers an attractive education discount, it would still be prohibitively expensive to provide separate copies for each student. However, installing Photoshop on one or two workstations in the photo lab might be an option.