I have cruised down to the Caribbean on several occasions and have seen many of the islands. Cruises are definitely your cheapest option as you can get some incredible cruise deals which include all meals etc. The downside of cruising is that you are only in port a day so your time on the island is limited.
It depends how deeply you want to explore each island. If you are only interested in island tours or seeing part of each island, then cruising works, but if you are looking for an in depth experience and to truly get to know each island, then back-packing or staying in Hotels would be a better - but much more costly way to go as you will have inter-island travel, accommodation and food to pay for.
For me, cruising works just fine as I don't feel the need to see more of the islands than you can see in a day. I hope this helps and bon voyage!