For formal use use"select", more colloquial "pick" or "make", the phrasal "go for a choice" belonging to the spoken language even more. If your phrases are not followed by anything else, then it is "select a choice" and "pick a choice". If there is, it's propably better to say "select/pick the choice, that..." If you prefer to use the verb "choose", "opt for" is also a good, more formal verb to use instead and one worth knowing. :)

You can also make a choice.

You could also use the verb form of choice, choose.