I power a nice size raido with good base sound, two neon signs and if I wanted 20 or so floureance “white” light bulbs. A good power convert should be at least 1000 watts I have one that runs on 1,500 watts and power boost at 3000 watts. You can get them for about 100 dollars or less at a truck stop. I got mine for 80, from private seller. Your marine battery where I live, if people buy the wrong battery they return it and the store will sell it at half price. I got a 120 battery for 55.00 Get a smaller one if you can..they are a beast weighing in At least 50 to 60lbs..but will run your radio and lights for days before you need to recharge the battery. I leave mine in the truck and run a long extension cord. I love sitting out at night with my neon signs and wave to customers as they see me with lights for the cart, table and such..like having a mini festivals of lights.. get lots of slow downs. but that’s your best bet for 160 with tax included.
I like to Show off a little LOL but that is the best system for you..but don’t use car battery..by the way, the set up I mention is only about 40 dollars more than a dewalt..and a dewalt will not power multiple things for 30 hrs or more before the battery even reaches half a charge.
That’s my .02 cents. Hope it helps.