Running as much as possible directly via 12v, rather than an inverter can make an important difference power wise. Many inverters use a significant amount of standby power, so if an inverter needs to on anyway ( to say run the DVD
player) the extra power cost of running a 12v TV via an inverter is not very high, but if you can run the whole system and watch a movie
without the inverter the reduced power consumption
can be worthwhile.
There is a slight risk running "12v" appliances
directly from the boat batteries as voltages can be above 14.5v at times. Most electronics
will cope with this fine, but very occasionally you can destroy equipment
The TV will have an audio output jack, usually 3.5mm if you are happy with just 2 channel. There are a number of very efficient T class audio amps that will run directly from 12v. They are very efficient with excellent, almost audiophile sound quality.
For $40 it may be the best solution.
However the Bose may have an active subwoofer running from AC in which cas you will forced to run the inverter. You can run the TV directly from 12v, but if the inverter needs to on anyway the power saving will not be great.