Super R-Type is actually a slight remix of the arcade R-Type II, with a couple of new enemies and stages tossed in.
In the credits, there is a track listing for all the songs in the game. It is as follows:
Start: R-9, To The Front
Stage 1: Solo Sortie
Stage 2: Counterattack '91
Stage 3: As Wet As A Fish
Stage 4: A Submerging Titan
Stage 5: Dream Of A Labyrinth
Stage 6: R Dance
Stage 7: National Anthem Of Bydo Empire
Boss Stage: Return Of The Creature
Ending: Escape From The Bydo Empire (Part 1) and Escape From The Bydo Empire (Part 2)
Novice Mode Ending: Try Harder!
Stage Clearance: To The Next Zone!
Game Over: A Combat Is Over
Continue: Blast Rock
Dunno if you can buy the soundtrack anywhere.