Learn Italian: Compro un francobollo per la lettera.

In Italian, the verb ending tells you who is doing the action. The -o at the end of compro means "I buy", so you don't need to say io unless you want to add special emphasis.

Could I replace la lettera with a pronoun here, like we're learning in this unit?

Absolutely! If you wanted to say "I buy a stamp for her" or "for you", you would use a tonic pronoun after the preposition per. For example, you could say Compro un francobollo per lei or Compro un francobollo per te.

Why is the word for stamp so long?

Francobollo is actually made of two older words joined together: franco (free of charge) and bollo (seal or stamp). It historically meant a mark showing that the delivery fee was already paid by the sender!

Why do we use un for the stamp but la for the letter?

The sentence uses the masculine indefinite article un (a) because the speaker is buying any general stamp, but uses the feminine definite article la (the) because they are talking about a specific letter they already have in mind.