The most common context in which the word rendere is used is definitely the second one, but it's a bit more complicated than that.
The main contexts in which the verb is used are the following.
Rendere as in giving something back to somebody (used in similar ways as the verbs ridare/restituire, the former being somewhat more quaint)
Mia sorella mi ha reso il mio libro.
As you pointed out, there is also a context referring to the action of causing to be or to become.
Mi stai rendendo la vita impossibile.
As for your example, there is a context in which the verb rendere would be used in the way in which you pointed out, but in a different way.
Il computer rende bene l'immagine
would not formally be incorrect, and I would use it for example when praising a PC with good rendering power, in a somewhat more technical connotation.
However, since you are talking about most common contexts, I would add that the most common way rendere is used in this context is when referring to certain characteristics of an artwork and whatnot.
In questo dipinto, ho cercato di rendere l'idea di amicizia fra i popoli.
Verga, nelle sue novelle, rende bene la vita dura dei contadini siciliani.
Personally, I would not say "ho reso una pittura", but I would instead say "ho fatto una pittura" or "ho fatto un dipinto".