If you are on shorepower, no need to upgrade the batteries at all.
A 12v compressor fridge will actually use less electricity than the old style absorption fridges and your battery charger should easily be able to handle it.
If you are going to be boondocking a bit, even then you don't need a huge battery bank. We have 2 stock 12v lead-acid batteries. Wok up this morning and still sitting at 12.6V.
What are the specs on your new fridge? Ours draws around 50watts when running but since it only runs part of the time, it really doesn't draw that much. Of course, some of this will vary depending on the temps...currently cool evenings so not a lot of fridge draw but balances with some furnace run time which wouldn't happen in warmer weather.