To dexters - nice post, I can't disagree with anything you have mentioned.
To the op.
I have played 1,000 hrs of archipelago maps on all levels with many different Nations. (England have more embarked unit movement.)
I have lost countless numbers of embarked units whilst exploring, well that is fine, probably true to real life of the age.
I very rarely loose an embarked unit whilst invading.
1 - Build a Navy.
2 - Bombard Cities/coastline, clear the sea along the invasion passage .
3 - Block ports.
4 - Escort embarked units. - If your Navy is powerful enough you may only need 3/4 embarked units.
When I play as England, I build three triremes ASAP build the Great Light House, find a city state, attack it until I have double attacks, ability to heal away from friendly territory and range,(now make peace with the CS) upgrade to Ship of the Line ASAP, now I have control of the seas for hundreds of turns.