The gerund is better here, stylistically speaking, but also in this example for a couple of complex reasons. But in answer to your question, I'd recommend using the gerund in this context for a CV or job description.
A couple of things to note:
Firstly, gerunds are nouns; they are just a particular form of noun that denotes an activity. The reason you'd want to refer to an activity using a noun is so it can serve as a grammatical function (subject or object). Interestingly, when acting as a grammatical function the gerund can take complements or adjuncts:
Landing planes with no pants on¹ is probably not a good idea.
The subject in the above is "Landing planes with no pants on".
Secondly, if you opt for the bare noun, then you should make both activities into bare nouns in your example:
Research and choice (of the optimal solution stack)
The reason is that and must take the same type of syntactic node on either side. If the left hand side is a noun, then so must be the right hand side. Of course in this example, both activities researching and choosing have scope over the complement the optimal solution stack (meaning it's the object of both verbs), in which case it is only the activity itself (whether it's a gerund of a bare noun) that is coordinated (separated by and). In other words, what this means is:
[Researching the optimal solution stack] and [choosing the optimal solution stack]
Thirdly, if you take the bare noun then you cannot retain the verb's complements in the noun phrase. This is why I have inserted of in the example above.
Choice the optimal solution stack
Is not licit. You must have of in there so that it conforms to phrase structure rules, so it is a noun phrase containing a genitive prepositional phrase:
Choice of the optimal solution stack
That said, I find the sentence research and choice of the optimal solution stack to be an awkward sentence, probably because my brain wants to read research with final stress (ruh-SEARCH, the verb) rather than with initial stress (REE-search, the noun), and this would violate the coordination rule.
¹Ambiguity totally not intended, but on re-reading, I quite like it!