Apocryphal's Intro to Frank Zappa
My own path to Zappa was to start with the material I already knew from what my father played for me. I bounced off Zappa when I was younger and came back to him when I was older. Developing a taste for jazz helped. Still, Zappa liked to challenge listeners (and performers!) so I had to sit down with it and listen over several times to really get an appreciation. I started with One Size Fits All, then I branched out from there both forward and backward in time. Eventually I narrowed down my selections to a couple of playlists. Below is the music on these playlists. Those marked with a ~ sign are maybe more experimental (depending on what you're used to) and those with a * are more mainstream/accessible. Those marked with ! are instrumental.
Golden Age Playlist 1973-1979
Over-Nite Sensation 1973 - this is a short album with 6 tracks, often said to be his most straight forward rock and roll album, and pretty accessible. The closest he came to commercial success.
* Camarillo Brillo https://www.youtube.com/watch?v=nllWDc8_9lw
* Dirty Love https://www.youtube.com/watch?v=zaXWG0fBYuk
~ Dinah-Moe Hum https://www.youtube.com/watch?v=u4hzVpYAP-U (Sexual content)
* Montana https://www.youtube.com/watch?v=smZA9Jv3qH0
Apostrophe (*) 1974 - technically a 'solo album' which means it doesn't feature the Mothers of Invention band, but might still have some members. Zappa is such a force I'm not really sure in matters which musicians he surrounded himself with, they were all good, and they all sound like Zappa, so I don't usually care whether it's 'solo' or not.
Cosmik Debris https://www.youtube.com/watch?v=wtx4ZJ1cwI0
*! Apostrophe' https://www.youtube.com/watch?v=zXP_pr7np-o
* Uncle Remus https://www.youtube.com/watch?v=yHIhsq9qHPk
One Size Fits All 1975 - This is a great album, maybe his most accessible. If you just want one Zappa straight up rock and roll album, get this one.
* Inca Roads https://www.youtube.com/watch?v=vAGVQM6IAKk
* Po-Jama People https://www.youtube.com/watch?v=u0T7QzuiYtI
* San Berdino https://www.youtube.com/watch?v=0yaX-a3kuCE
Zoot Allures 1976 - I tend to prefer the instrumental tracks on this one.
*! Black Napkins https://www.youtube.com/results?search_query=zappa+black+napkins
*! Zoot Allures https://www.youtube.com/watch?v=fdQmhhi5cLI
Sheik Yerbouti 1979 - This was super productive year for Zappa with 5 albums - 3 of rock and roll (one of those a double issued in separate issues) and his first 'classical' album. Sheik Yerbouti was the most straight forward rock and roll album of the year, and on some lists it's considered his best ever album. I won't post any tracks - just listen to the full album after you've checked out the tracks listed here. There's a lot of irreverent and sexually charged material on this album, so be cautioned.
Joe's Garage 1979 - Another candidate for his 'best ever album', Joe's Garage is a concept album that tells the story of a guy names Joe who forms a garage band with his buddies, but gradually gets chewed up and spit out by the system, which is represented by the narrator on the album, a sci-fi 'big brother' type figure called the 'Central Scrutinizer'. Zappa placed the narration of the 'Central Scrutinizer' between many of the tracks to introduce them. He voiced the character by whispering into a loud-speaker and recording it. Sometimes he cracked himself up with his own writing, so the moments where he laughs at his own humour is also captured. Conceptually, I think this is a really brilliant album. It was originally released as two separate LPs, Joe's Garage Part 1 and Joe's Garage Parts 2 and 3. Or in CD format it's a single CD package with two disks.
* Joe's Garage https://www.youtube.com/watch?v=_oH8u9PxWJo This track changes tempo etc. a few times, so listen through it. This chronicles Joe's beginning in the garage.
*! On the Bus https://www.youtube.com/watch?v=dcN89Xd2lPY
* Lucille Has Messed My Mind Up https://www.youtube.com/watch?v=3-nWfSJ9ab0 Joe falls in love with a girl who hooks him on drugs, then gets dumped.
~ A Token of My Extreme https://www.youtube.com/watch?v=gUqEj2xZFw8 Looking for meaning, Joe falls in with the Church of Apliantology, headed by a guy named Ron. To me this track sounds like the intro to a song that came out in 1976 on One Size, called Sofa No 2: https://www.youtube.com/watch?v=GXkJ2xErjy0 Zappa was more popular in Germany (where they weren't offended by the lyrics) than at home, hence several German references in his music.
*! Watermelon in Easter Hay https://www.youtube.com/watch?v=_3cu8sDa90Y often said to be Zappa's best guitar solo.
Sleep Dirt 1979 - This album is mostly instrumental and has some great tracks. I didn't discover it until late because it isn't on any of the 'best zappa albums' I saw. But I can't explain why.
! Filthy Habits https://www.youtube.com/watch?v=5ugJrB2jYm0
! Sleep Dirt https://www.youtube.com/watch?v=R7_kuDyuBwo
!~ The Ocean is the Ultimate Solution https://www.youtube.com/watch?v=zCNRgfkeWXs
Older Instrumental Material:
Hot Rats 1969 - The whole album is great, a fusion of hard rock and jazz, sometimes pretty acid, but it seriously rewards repeated listens. Considered by many Zappa's best album.
*! It Must be a Camel https://www.youtube.com/watch?v=4xg_elzHQz8
Burnt Weenie Sandwich 1970 - Some great instrumental tracks here, and one of my all time faves below, which changes pace and sound 3 or 4 times through the song so listen to the whole thing:
!~ Holiday in Berlin Full Blown https://www.youtube.com/watch?v=FccwMLnWPls
The Grand Wazoo 1972 - Another classic solo album from his 'fusion trio' and partner album to Waka/Jawaka.
!* The Grand Wazoo https://www.youtube.com/watch?v=4ceVq2v3nVs
!** Blessed Relief https://www.youtube.com/watch?v=x-Qk8VxUwuM
!* Eat That Question https://www.youtube.com/watch?v=jymHINLcjlw
That ought to keep you busy - have fun!