In case of multiplicity higher than singlet Gaussian will automatically switch to UCCSD, if you want to calculate open shell singlet you may specify UCCSD with multiplicity 1. Restricted open-shell has its own advantages and disadvantages, I personally prefer unrestricted calculations whenever its possible.
Small basis sets like 6-31G, def2-SVP, cc-pVDZ are meaningless in combination with post-HF methods like MP2 and especially CCSD. Abinitio methods has very slow convergence in respect to basis set, so results with small basis set will be so approximate that there is no point to use so expensive method as CCSD.
I would compare it with sending rocket to the moon using for identification of "north" location of moss on the trees.
Triple zeta would be already better, doublezeta-triplezeta extrapolation - enough for chemical accuracy in majority of cases (one need hierarchical basis sets, so no Popple).
I would recommend cc-pVXZ basis sets or their augumented, minimally augumanted or core-weighted modifications, depending on the task.
CCSD is a keyword that can be used in Gaussian or in dominant amount of other computational programs for applying the CCSD method.
Yes, its abbreviation from "coupled cluster with single and double substitutions" or "coupled-cluster methods where the cluster operator contains all single and double substitutions" or "Coupled cluster with a full treatment singles and doubles (single and double excitations)". there's not much difference in these formulations.