Is the minimum criterion for life a single cell? It seems that self-replicating RNA is not enough, but I don't know.
What would be the most basic cell that could fit this criterion and what cells today would be most similar?
I think it's a mistake to assume that there is such a point. All plausible seeming models of abiogenesis currently under consideration involve evolutionary processes long before they reach the stage we'd consider alive.
Evolution will occur whenever there is (a) replication-with-error and (b) selection (simplifying slightly). This is the case with a self-replicating RNA. It is replicating, but those replicates can be imperfect. Imperfections in replication that improve its ability to replicate will be favoured. That's evolution.