I personally would not of purchased the cards until later as having more instruments and luck is going to help you more. As the instruments and the mission list expands, it becomes less of an issue.

So here is a suggestion. Each music lesson uses specific instruments and depending on the rarity, it will boost the skill points you get from music lessons. Duplicates also help so you may want to focus on 1 or 2 instrument types. I personally see those cards only useful for fans at your current stage and an investment into instruments would help you more long-term.