When we bought our boat it had a microwave oven and a lousy old charger. This was in 1998, back before low power draw 12V TVs. We wanted to add a TV/VHF combo unit for our kid. So I did my homework and figured a Freedom 15 with a Link 2000 (which could control the charger and inverter side of the I/C) was pretty much a wash as far as cost, and a lot less wiring connections than a standalone charger and separate inverter.
Times have changed. The Links are no longer made (drats) and the Freedom series can't, as Maine Sail said, be controlled remotely.
If I had to do it all over now, I'd get a good charger that can equalize batteries) and a separate inverter.
A separate inverter can be wired a few ways:
1. Just use the receptacle on it, and don't feed it back into your house AC power. Simpler wiring, no need for a special AC input switch (Blue Sea 8032 or equivalent).
2. Just wire the inverter into one receptacle on board.
3. Do a full monty and install the inverter as part of your overall AC electrical system with the 8032 switch.
If you do, regardless of how you do it, do an energy budget and find out what size battery bank you need for your situation and proposed use. A few bags of popcorn is a lot different than three hours of TV.
Or, as suggested, just get a 12V TV. Think how much $$ you'll save!
The West Marine online Advisor has very good electrical system information.