Can you propose a model theory and basis set to be used in the computational studies of cyclic carbenes (cycloprpene carbene). Is it okay to apply to for both singlet and triplet states?
First, research the literature so you won't double the existing papers. See e.g. http://www.sciencedirect.com/science/article/pii/S0166128099000329
Since your system is very small, you can go to very accurate methods (depending on available machines). Complete basis set calculations has been done 17 years ago (see the paper above) so now you should be able to do basically anything, including CCSDT or perhaps even G1-4.
You should definitely try both singlet an triplet, even if just to see if your methods of choice can reproduce experimental energy difference.