Motorola Talk-About FRS/GMRS radios will give you fairly good power and range for a reasonable price.
There are few "affordable" radios, that you don't need a license for, that will work "everywhere" on a ship but these will work in most places. If someone is in the lower parts of the ship and someone else is on the top deck you may not be able to talk.
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Good question. We have never seen rental radios on any cruise. There are several sets of radios that are fairly good. Many though will incur issues aboard a ship due to the construction of the ship. Finally please be aware that ere are some very strict laws in some countries pertaining to these radios. They are considered a "security issue" in certain places around the globe. This would mostly be applicable if you took the radios off the ship.