Ex: "ho deciso di portare una bottiglia di vino."
"Vado a prendere la macchina."
"Voglio __ chiedere il suo nome."
So, are there any tricks or reasons behind different choice of preposition? Or I just have to memorize them?
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I'm afraid you have to memorize them.
Here is a list (quite complete, I hope) of the possible cases; as you can see there is not a simple rule or trick or reason. Moreover, the verb sapere has different rules depending on the meaning.
so di avere sbagliato
The following verbs require the preposition di:
accettare, cercare, credere, decidere, dimenticare, dire, domandare, evitare, finire, impedire, meravigliarsi, pensare, permettere, pregare, preoccuparsi, proibire, promettere, rendersi conto, ricordarsi, rifiutare, ringraziare, rischiare, sapere (in the sense of knowledge), scegliere, smettere, sognare, sperare, tentare, valere la pena.
The following verbs require the preposition a:
abituarsi, aiutare, andare, continuare, divertirsi, esitare, forzare, imparare, impegnarsi, incominciare, incoraggiare, insegnare, invitare, mandare, mettersi, persuadere, prepararsi, provare, rinunciare, riuscire, servire, stare, uscire.
The following verbs require no preposition:
the verbi servili potere, dovere, volere; and:
amare, ascoltare, desiderare, fare, guardare, lasciare, osare, preferire, sapere (in the sense of being able), sembrare, sentire, vedere.
Prepositions in front of an infinitive are not related to the infinitive verb itself, but they are needed to specify the type of information conveyed by that non-main (i.e., not the verb nor the subject) part of the phrase.
In your examples:
Edit: TL;DR answer is yes, you have to memorize them, but they don't come from the verb you are putting in the infinitive mode, but from the ones that are used for the part-of-phrase you are putting the infinitive verb into.
Edit #2: Adding a link that may be useful to the OP (http://www.zanichellibenvenuti.it/wordpress/?p=4401) it contains a list of main verbs and the required preposition for the infinitive verb associated. There are 4 main groups: verbs not requiring prepositions before an infinitive, verbs requiring "A" (and a "figurative static place" as part-of-phrase, which is why in some verbal situation the preposition may be replaced with "NEL"), verbs requiring "DI" (and a "specification" part-of-phrase), and verbs supporting both "DI" and "PER".