when I wanna' call someone on the phone, let's say a friend of mine, would I use "Je te rappeler" or "Je t'appeler"?
"Rappeler" is "calling back / calling again". So if this is the first call, use "appeler" : "Je t'appelle."
Generally speaking, prepending a verb with "re-" or "r-" mean "doing the action again", like "revenir", "reprendre", "refaire", "racheter".
If you need to cut mid-call and plan to call the person again, you would say "Je te rappelle (dans 5 minutes)".
"Rappeler" is not used for "to call" and the verb must be conjugated, it cannot be in the infinitive.
When the call is going to be made some time after the person is being told they are going to be called, the present and the future can be used; there is just one exception.
Nous sommes aujourd'hui vendredi, je t'appellerai/appelle dimanche dans l'après-midi, ce qui te donnera deux jours pour réfléchir.
Je t'appellerai/appelle demain.
Je t'appellerai/appelle dans un instant.
Je t'/appelle tout de suite. (The future is not possible here because "tout de suite" denotes a very short instant; if the future were used the sentence would mean something else (in an other context).)