Huge amount of factors to consider. Depends on time-line, budget and how talented said programmers are - and of course, the scope of your project.
Our studio has five teams of four, with approximately two dedicated programmers and two artists on each team. Obviously, those are lenient terms as everybody has to do some crossover (which I’m happy about, tech artist ftw :D). To give you some idea, two teams are working on complete games for PS4, my own team is working on a “AAA” title for tourist attractions, while another is working on a VR experience for a similar market.
We do have one secret weapon though, there’s a guy who works with all of the teams and has 12 years experience at EA on Burnout / NFS titles. I’m pretty sure most of us would be up ****-creek without him. I guess what I’m saying is that with the right people you can do magical amounts of work in a (relatively) short period of time. Our development cycle is approximately one year, whereas the two games teams are aiming for two years. That’s from concept all the way up to shipping, and founding a business / getting investment of their own all in the same time.
Whoever you plan to hire, pre-prepare a series of programming tests that they have to take to be considered, and request a portfolio. The tests are the important part, anybody can lie about what they’ve achieved over the internet.
Again, this depends on your project but our teams have a mix of the following:
- Animators
- Programmers (C++, C#, Java and of course Blueprint. C++ and Blueprints are the only ones we use).
- Artists (Modelling, Texturing & Basic Shader Knowledge)
- Technical Artists (Mixture of skills in artwork, programming, FX and advanced shaders). <- Rare but useful. I should know, I am one
(and biased) - Technical Designers (People who have an eye for design, but also the knowledge (but not the know-how) of what can be achieved).
Level Designers, User-Experience etc. are all things you can skimp out on. You’ll be surprised how much people can diversify when they have to 
One final piece of advice, Game Jams are seriously good ways to judge your teams’ proficiency!