Each state has its own requirements for solar installers.
In Illinois there is only one requirement to install solar. A solar installation company either needs to have a Distributed Generation Certification through the Illinois Commerce Commission or be working with a subcontractor who has this certification
In addition a certified electrician is required to pull permits for the work. This can also be the installer or a subcontractor.
Some additional credentials that may reinforce the quality of the installer are;
If your installer is not an electrical contractor or doing 100% of the work, then they will be subcontracting some of the work. You should find out who this is, what their craftsmanship warranties are, and possibly ask for referrals. If any of the work is subcontracted you should make sure to get a lien release before the final payment so that they can't hold payment against your house or building.
Items that should be in your contract: