Keep in mind that the fuse or circuit breaker you are talking about is there to protect the battery cables from short circuit. Your batteries can probably produce a couple hundred AMPS for a short period of time and of course your 45 AMP Converter/charger can produce 45AMPS of DC current.
I have three batteries in my battery bank and when I am using my PD9260C 60AMP smart mode converter/charger in charge mode I will see around 52-53AMPS being drawn by the battery for the first 15-20 minutes of the initial charge cycle.
I would think you should have a fuse or circuit breaker rated at the highest output of your converter/charger unit. In your case higher than 45 AMPS.
We do alot of camping off the power grid and I would say a minimum battery capacity should be around 220AHs. This would require a couple of batteries at a minimum in my thinking.
You may want to add a 300-400WATT PURE SINE WAVE Inverter down the road to run your home entertainment items and cell phone and computer chargers etc. Once you start doing this you most likely will want to run some other low wattage items from the INVERTER. Inverters love large battery capacity...
We get by very successful using our 255AH battery capacity but do have to recharge every day at 8AM during breakfast when allowed to run my 2KW Honda generator at most campgrounds. Once the battery bank is back up to its 90% charge state than we can do this all over again for the next day/night run off the batteries.
Just my thoughts...
Roy Ken