The Mediterranean and the Caribbean are the two most popular sailing destinations in the world, and they could not be more different.
The Caribbean offers reliable trade winds, warm water, and a sailing culture built around the charter industry. The infrastructure is excellent. The passages are short. The anchorages are protected.
The Mediterranean offers history, cuisine, and scenery that the Caribbean cannot match. Sailing through the Greek islands, the Croatian coast, or the waters around Sicily connects you to thousands of years of maritime history.
My recommendation: if sailing experience and relaxation are your priorities, start with the Caribbean. If culture, food, and history matter as much as the sailing itself, the Mediterranean is worth the additional complexity.