I was thinking of some sort of battery that I could charge at home and take outside but must be able to store a lot of electricity like be able to run 600w for 18 hours. I think a generator will be too expensive.
There are only two real choices, batteries, or a gasoline/diesel driven generator. To store that amount of power via batteries, you would need about 11 large auto batteries. A 100 amp-hour lead acid battery can store about 1 kW-hour, and you need 0.6kWx18hr 11 kW-hour. You need marine deep discharge batteries and they cost about $300 each, plus charger costs, so a generator would be cheaper. You can get a 800 watt generator for $300. OR if outside home is literal, you can run a long extension cord.
You can buy battery packs with built-in chargers that you can take around. But you do not mention what voltage you wish to have out of the pack. A 12v pack would put out 50 amps to make 600w. The problem there is that it would disperse 50 amp-hours per hour. You would need a 900 amp-hour capacity unit of many batteries. That would take a pickup truck to move, and quite expensive to buy the 25 batteries. If you wish to make 110vAC at 600w, that would be only 5.8 amps AC current. There are many inverters that can do that, not too expensive. But you would need to hook it to an automobile with the engine running, since the amp-hours or even more would be the same from the 12vDC car battery. Running the car engine for 18 hours would surely ruin something under the hood (engine, voltage regulator, alternator, fuel system, battery?) The amount of energy you require over time is enormous. It would be equal to a tank of gasoline, or about 90 sticks of dynamite. My Nissan LEAF electric car's battery can store 27KW at a time, but takes 10-20 hours to charge, depending on voltage supplied. That would be more than enough for your requirement, but do you have $35,000?
Tap into your neighbors power line and run it all day. When they ask if your electric bill went up just say yeah, they must have raised the cost per unit of the electricity.
