The first actual record I bought was a classical music collection called “Music America Loves Best”. Still love that music. I think I was about 10 or 11.
The first non-classical album I bought for myself was a tie, because I bought at the same time: Depeche Mode “Some Great Reward” and Sting’s “The Dream of the Blue Turtles” (yes, on vinyl)
I bought my first album when I was seven–I brought all my rolled pennies (my dad used to give me all the pennies from his pocket every night when he came home) in my white wicker box of an Easter purse to the record store to purchase my very first full size album: Sergeant Pepper’s Lonely Heart’s Club Band. I think it was less than two bucks new.
I’m so glad it wasn’t The Archies! 
A Hard Day’s Night. Which I had to keep at the neighbor’s because my dad thought spending money on music was a waste.
“Sergeant Pepper’s Lonely Hearts Club Band” – in mono.
Second (and this will come to no surprise to those familiar with me here on the SDMB) was “Urban Spaceman” by the Bonzo Dog Band.
I’m still delighted at my choices.
I used my allowance to buy the album ‘Meet the Beatles’ in the grocery store no less for something like $1.77. Yup, it was a new release.
Cassette: AM/FM by George Carlin
Album: Partrige Family
CD: Aja by Steely Dan
I think it may have been a Beatles bootleg album called “More From The Fab Four,” that I saw in a head shop. If not that one, then it was probably one of The Beatles’ albums, like “Abbey Road.” That was a long time and thousands of albums ago!
Steve Miller’s Book of Dreams.
Second album was Fleetwood Mac’s* Rumours.*
My older sibs had all the Beatle’s etc.
Dare I admit it? … Up to Date by The Partridge Family
The first album I owned was a cassette of Metallica “Metallica” ( the black album) in the 7th grade. It is still one of my faves.
I used birthday money from my 10th birthday to purchase The Cure’s “Kiss Me Kiss Me Kiss Me” (their most current album at the time) on cassette.
Surfing by the Ventures - 1963.
Sheryl Crow’s Tuesday Night Music Club. Second was Amy Grant’s Heart In Motion. I think this was 1993. I doubt I still own either.
Soft Cell. I remember it distintclty… A couple weeks later The Rise and Fall of Ziggy Stardust and the Spiders from Mars. Which proved more fruitful (ahem).
“Here at Last – Bee Gees Live.” It was $9.99 at Twin Fair. I had to babysit for 5 hours for it.
I still love that album.
Huh? No Beatles for you? My world is cast asunder…
**The White Album
**
So there. Pffffttt.
Danny Elfman’s Music For a Darkened Theatre (a collection of his film score themes), on cassette. I was in 7th grade, so this has to be 1991-ish, right before I really got into rock and popular music.
(The Diabolical) Biz Markie’s The Biz Never Sleeps. Woulda been 1990 or so.
First one I asked my parents to buy - Bill Cosby Is A Very Funny Fellow – Riiiight! (the one with the Noah’s Ark routine).
First one I purchased myself - Tapestry by Carole King, on cassette. I have since bought it on CD and it is on my computer’s hard drive and my 40 GB Zen.
Sinead O’Connor’s I Don’t Want What I Haven’t Got. I actually got my first copy as a Christmas present in the 8th grade, and I listened to the tape so much that I broke it. So I saved up the cash (by doing extra chores) and bought a replacement…which was about $11.
I still listen to it to this day.