I agree with Tomaz on the Sunsail base in Antigua and the whole English Harbour (with Falmouth nearby) is historically cool.
Do You plan to self-provision?..........that could influence your choice of charter companies given easy availability of a large supermarket near Horizon (Jolly Harbour). I rented a car & had time before my Sunsail charter so it did not impact me ...........and I still used supermarket later in the charter @ Jolly Harbour when we re-filled our water tanks &
dinghy fuel.
To Your questions:
1) Boat Selection - Decision points......... Layout= cabins/head/galley, + Gear/sailplan/tankage..........that will work for you and crew........LWL will help given distance & open water you plan to cover...
2) Charter Co selection - you don't seem to have a preference one way or the other..............in that case it comes down to boat choice/availability, cost and support.........also note ..........SXM base differences - Sunsail at Oyster Pond (interesting entrance - do you like to surf?) or Horizon @ Simpson Bay - don't forget bridge opening timing
3) Did you plan to stop in Barbuda or fall off and head straight to Nevis?
Barbuda is unique & a complete get away......got more info if you need.