Learn Portuguese (Portugal): Podes escolher qualquer disco.

No, qualquer stays exactly the same for both masculine and feminine words. Even though disco is masculine, if you were talking about a feminine word like música (song), it would still be qualquer música.

How would this sentence change if I wanted to say "any records" in the plural?

You would say Podes escolher quaisquer discos. The word qualquer is highly unusual in Portuguese because its plural is formed by changing the middle of the word, becoming quaisquer.

Why is escolher left in its basic dictionary form?

Because it immediately follows another conjugated verb. In the phrase Podes escolher (You can choose), the first verb (Podes) is already conjugated to match "you". Therefore, the second verb (escolher) must stay in the infinitive (the unconjugated form).

How do we know this is the informal "you"?

The verb Podes is conjugated for tu, which is the informal "you". If you wanted to say this to someone formally, you would drop the "s" and say Pode escolher qualquer disco, which uses the formal você conjugation.