RV Plugged Into Household 110 Circuit

I'd go for a multi-stage charger that supports a desulfate mode (it is a pure shame that most new rigs come with single stage units), and just leave it plugged into 120VAC. This won't allow you to run the A/C, but it will keep everything else charged. Some rigs may even keep the chassis batteries charged. If not, you can always plug a Battery Minder in for that.

Don't forget to run the generator every few weeks though.

No issues as we have been doing this for many years. Our rig's converter has smart charging technology built in and does a wonderful job of keeping batteries charged and conditioned without fear of boiling batteries dry, although I routinely check battery fluid levels as part of my maintenance regimen. Best not to run AC unit as voltage drop may cause damage to compressor, but most everything else will run fine up to your 15 amp limit.

Unless you plan to run the AC while in storage, you do not need anything other than a basic 15 or 20 amp outlet.
Mine stays at a rental storage facility. I have to pay extra for electric so it stays plugged in any time it is there, which means all winter. It is 15 amp.
I can run one 15k AC on 20 amp outlet, but not on a 15 amp outlet.

We added a 30 amp to our elec. post for our class B, we live in a park model so this was an easy add on. Be very careful not to keep a charge on the batteries to run the water down. If you do need to add some water after charging, only fill with distilled water. I agree with the others here that you only need to set up to charge about once a month while storing if there is nothing running the battery(s) down.

Suggestion put 50 in - just in case you need it for a new unit some day you will be ready.

First our 5'er and now the MH have spent their "life" plugged into a 20amp outlet in my shop. I have ran A/C on a very rare occasion but mostly just let it kept battery charged and fridge cold. I'll also run a 1500watt electric space heater overnight if temps are marginal as far as freezing and I've got water in plumbing system.

Batteries do not need to be charged all of the time. Overnight once a month should be enough. Maybe you are keeping refrigerator cold?

As above have stated. Also remember to check the water in the batteries occasionally. They have a tendency to sometimes boil dry if not checked once in awhile. JMO

You are now on limited Shore Power.
You will be limited to amps that are feed into that receptacle
from the house circuit breaker. Most likely 15 amps.

I keep mine hooked up the same way.

The Converter keeps the house batteries charged and I added
a small battery maintainer that I plug into the coach that
goes into the dash power port and it keeps the chassis battery
topped off.

You will have limited use of items in the RV. Such as as the heater fan, TV, refrigerator. Heavy amp items like the A/C, or combinations of several may/may not work as the house breaker will trip.

Many RV have monitors, etc that run off the chassis battery.
After several weeks it is not unusual to find the chassis battery
discharged to were it will not start. That is why I have the small
battery maintainer inside.

I starred this almost 2 years ago,
with no problems.

Other than the limited current you will have no other issues and the battery should charge as it does on a 30A service.