You are welcome Cannons, I haven't added TrekkieELO's to your list until he classifies them.
Many of the ones I thought of are added already but here are a couple more.
Classical, Rimsky-Korsakov. Specifically his Suites, they are a great entry point into classical music.
Jazz, George Benson. Breezin' or In Flight they are my favorites.
Blues Rock, Pat Travers. His early albums are really good blues rock, later on he became a little more mainstream. His ST debut and Crash & Burn would be my picks.
Folk Rock, Gordon Lightfoot. Summertime Dream I play this one all the time.
Psychedelic Rock, Hawkwind. Early Hawkwind is the best, In the Hall of the Mountain Grill is really good.
Punk Rock, Tom Robinson Band. His album "Power" is one of the best ever done in the genre, I rate it just behind London Calling by the Clash.
There Cannons, not only an artist but a specific album recommendation to go with them.