A hair dryer will eat up batteries pretty quick. Mine will draw over 100AH, which won't last long even with my 300AH battery bank.
The battery bank size will depend on how long you want to go between charging.
Salesmen probably know little about boondocking or your needs. Many people who boondock don't feel the need for 120V AC power without a generator.
A 1500w continuous 2000w surge inverter should give you all the power you need. I have the xantrex x-power 1500 and it works very well. I have it wired thru a pair of xantrex inline transfer relays to power all of my general outlets.
An auto transfer switch is a good idea so that you can power any outlet with the inverter, but shore or generator power will overrode the inverter. You won't want the microwave, a/c, fridge, or converter on the inverter circuit but the remaining circuits can be.
At a minimum a pair of 6V batteries is what you want. If you use the inverter a lot you will need to recharge more often, or have 4 6V batteries installed... But they will take 2x as long to recharge from a 50% SOC.