The Commonwealth navy may have been very effective at the height of it's power, but by 1660 those days were long gone, and the navy had fallen far .
Tedder's Restoration Navy gives details of the state of the fleet at the restoration. Not a pretty tale. Most ships had not been paid for many months, even years. A great number were reckoned foul, in need of repairs, unvictualled. Most were laid up. In essence, the fleet in 1660 was a ruin.
So the money initially voted by the Restoration parliament all went on just paying off the arrears.
As to commanders, it's hard to see any other names that would have been notably better than York, Rupert and Sandwich, OK, Albemarle, though a competent soldier was a disaster at sea.But York was competent and effective. Ditto Sandwich. And Rupert, at his best , was brilliant. Patchy, but at a melee battle like Lowestoft , where he could treat ships like cavalry squadrons, he was probably without peer. I don't think Charles could have found any better commanders .