I'd like to see Memphis trying the Gasol-Thabeet combo. Thabee's quickness is very impressive, I believe there's a chance that pair could work.
Mayo isn't a good wing, but he can be an excellent complementary player for a contender more or less in the same role Mo Williams has in Cleveland - I believe he'll be a better player than Williams.
Rudy Gay can be a cornerstone for a contender if he develops his non-scoring contributions. I wouldn't be very optimistic - I think it was wise from Memphis to not extend his contract. A Monta Ellis type of contract is a threshold they shouldn't surpass.
I'm not sure about Randolph's role. Can't see any, except allowing them to give the young players some playoff experience and increasing their trade value. Too much of a high maintenance, one way player. They can probably use a player like him in the future, but they're not there yet.