You can get records in three ways:
1) buy them from Amanda (the cat on the plane does not sell records, only the chick Amanda). There is a different selection of records in each episode.
2) get them as a bonus from the characters in the game for completing their cases
3) if you get lucky, you can get a record in the box delivered to your door in Episode 2. Every time you play the Episode you get a new package with a rare item.
I hear you will get five free records with the free DLC "Spy Fiction".
Getting five records will be easy, getting ten will be easy, getting twenty will take some time.