I'm not 100% certain, but I'm reasonably sure the very first album I purchased with my own money (hail, paper route brother!) was the soundtrack to the animated Transformers: The Movie on cassette. It wasn't the first cassette I owned, because I'd received tapes as gifts for years, but I'm pretty sure that's the first album I deliberately saved up money to buy. It's been thirty-some years since then though, so I could be wrong. Other potentials are AC/DC's The Razor's Edge (although I'm almost positive this was a birthday or Christmas gift), the Scorpions' Best of Rockers 'n Ballads, and Neil Diamond's Twelve Greatest Hits.
Don't judge. ;)
the Transformers cassette was actually really good, i remember that. It had one of my favorite Weird Al Songs on it called "Dare to be Stupid"
Don't ever be ashamed of Neil Diamond... his stuff rocks.