The buzz is from the inverter. It chops up the dc and steps it up. It then shapes it into a sine wave. You can make a cheap inverter that does a poor sine wave (buzzy on audio equipment) or a more expensive inverter (hopefully closer to a real sine wave). Best thing is to try one to see if it plays nice with your amp. Lithium batteries are lighter but you need a proper charger for them. You would want to get them at the proper voltage for your inverter.
Radio controlled model car/airplane people know about getting the most power in a little package. Without knowing how long you will be playing between charges, the power consumption of the amp, the efficiency of the inverter, it is a wild guess to select a battery. Looks to be a nice little amp.
If it were me I would have a tech (actually I would not need a tech, I am one of sorts) measure the voltage the amp runs on and get a Li pack made up for it (RC guys again) and use a RC charger. You would get longer play time out of the batteries as you would not have the inverter losses or the losses converting the 230V back down to a voltage the amp runs at.
Just came across this.
http://www.streetmusician.co.uk/batterycalculation/