Can anyone clarify why the infinitive of the verb sometimes has à before it, another time pour and sometimes nothing?

Question

I'm learning to play the guitar. J'apprends à jouer de la guitare.It's quite difficult because I'm a bit old to start [learning] an instrument. C'est assez difficile parce que je suis un peu vieux pour commencer à apprendre un instrument.I'm happy with my progress, and I hope to continue like this!Je suis content de mes progrès, et j'espère continuer comme ça !

Accepted Answer

Bonjour John,
To supplement Maarten's great answer, here are two more links:
- verbs_pour+infinitive_in-order-to
- verbs_à-or-de
'commencer à + infinitive' is more common than 'commencer de + infinitive' as the latter is used mainly in literature or formal written work. 
I hope this is helpful.
Bonne journée !

Answer

verbs-à+infinitive  
verbs-de+infinitive
“Pour” changes the meaning of the sentence, it is there to indicate “old for/in order to be”.  Commencer, as with many verbs in French, requires a preposition - à or de - preceding a following infinitive.