[Gray Adams]

Some people are recommending Solid Edge. I only have limited experience with it (half of one course designed to teach basic CAD...), but I hated that software with a passion. It felt very limited and clunky. Support for it was difficult to find and I've never even heard of it being used in industry. Others may disagree, but I see no reason to go with Solid Edge over Solidworks. Synchronous modeling isn't that important, especially for FRC applications.

If you can get legit copies of NX, that would be ideal. NX is some of the best modeling software I've ever used, and its widely used at larger companies. Solidworks is pretty universally used (many large companies use or used to use it for smaller projects that don't require the stability or PLM capabilities of NX+Teamcenter), so that would be a second choice. It's also much more intuitive and still pretty powerful.