The coin state "stealth (CT – Confidential Transactions)" is a halfway point from basecoin (public) to ringct (private address and private amount).
When automint was programmed zerocoins were fully private too, so the automint routine mints directly from whichever cash bucket the sufficient amount is found (first try, RingCT, second try CT/stealth).
If you use the optional setting to enable minting from basecoin it will mint directly from basecoin, which if a spy modifies the code of their wallet they would be able to track that zerocoin.
So manually minting is the recommended way now, enabling you to move your veil from basecoin to stealth and then to ringct before using the mintzerocoin command.
As minting each zerocoin costs 0.01 Veil you can afterward spend directly (and without fee) out of zerocoin to (basecoin using a bv... address or to stealth with an sv... address).
You don't need to move the zerocoin anywhere just to stop staking. Just fully locking the wallet will stop staking, or click the "staking" slider switch.
There's no reason to completely zero your RingCT because any time you want to mint another zerocoin you will need some small change for the minting fee. In the long run we will be moving to staking just in RingCT, so zerocoin will be eliminated.
The advantages of RingCT include the ability to spend a large amount in a single very fast transaction, so long as there aren't too many dust-sized RingCT inputs.
Large amounts of zerocoin in a spend are split into transactions with a maximum of twenty coins. This means that the most common type (denomination) of zerocoin being spent (tens, as that is what stakers get paid in) the maximum in a single transaction ID is 200 Veil. The wallet auto-splits these, but a 2000 Veil spend to an exchange using only ten denomination zerocoins will have ten different transaction IDs.
If you want your wallet to send a single TXID for an exchange deposit you might want to send to your own stealth address from your zerocoin first, and then send to the exchange's address in one transaction, or use 1K coins.