First off I assume you're talking about blockchain.info web wallet (based on your description it sounds right)
I think quick send will include an appropriate fee that is required by the protocol and should also be picked up by miners without much delay.
Custom send is just the "advanced" version, you can set your own fee (lower if your brave and don't mind waiting possibly several days)
You can choose where the change goes, with most Bitcoin wallets, a new address is used every time you generate change. With "custom" in blockchain.info you can ask change to be sent back to an address that you have used before. This might be handy for a paper wallet, but it is not recommend to re-use addresses if you can avoid it.
Don't quote me on this, but I should expect that blockchain.info will not allow your change to be "eaten" as a transaction fee. I highly recommend you read their FAQ/support.
You may have read somewhere that people have lost a lot of bitcoin because they didn't specify a change address -- this is possible if you're using hand crafted transactions, e.g. brainwallet transaction generator. If you are operating a low level it's possible that you forget to specify where to send your change, and the protocol assumes that this is your "fee". But with any respectable wallet software/service it will handle your change correctly.
It sounds like you might want your change to return to your paper wallet, so if you have this address loaded in your blockchain.info list, then use "custom" send and specify your change to go there. Don't forget to set a fee if you're using custom, if you're only sending to 1 address, and 1 change address then 0.0001 BTC should be enough, but 0.0002 would cover all bases for most basic transactions like that.
Hope that helps!