Since you have a floating charger, determine the specs of that charger 
to see exactly what type of battery, and how much battery capacity it 
will handle. Then buy accordingly, but with a bit of planning.

A recent silent key friend of mine used such a charger along with a 
200 amp hour marine battery from WalMmart to power his 50 watt 2 meter 
station full time.

He was retired, and on the air a bit more than average. Nevertheless, 
he would consistently get 2 weeks of operating between charges.
If you go with a battery of that much storage capacity, you must know 
and understand several things.

#1. Improper handling of such a battery can easily be fatal.

#2. improper handling can burn down your house.

#3. Mostly for the two reasons just listed, but also for some hazzard 
conditions relating to poor ventalation during charging, do not keep 
the battery inside your house. Interstate Battery, and most other 
battery suppliers sell special container boxes for housing these 
batteries. Set it as close to your radio as possible, but out doors, 
in one of these weather proof boxes.

My friend kept his on a porch that was just outside his shack, and 
used about 10 feet of very large red and black paired cable to get the 
power inside to an Anderson Power Pole box.

There is now some interest in my area in using this type of setup 
along with a solar pannel.

While this much battery may be more than you want, it is a serious way 
to keep a station available during a power outage, with or without the 
solar pannel.