Hey plee welcome to this forum
Battery....20 dollar one from walmart...they are 230cca i believe and they also have one with slightly more cca thats like 10 bucks more. Ive used both no problems. The HH150s already have the 39T sprocket unless its been swapped for the 31T but it came with 39T from the factory. 39T sprocket is defiantly worth it if for some reason its been changed.
I run A12 cams in all of the ones ive done upgrades to. Tried A11 and it broke the valve springs ina stock head. Have never had luck with the 30mm intake and the uper cross bar for the engine mounts was in the way on mine. 150cc scooters are the same motors as the older buggys for the most part but there is several different variations of the gy6 transmission/gearbox.
This should be yours....top circled one is fill and bottom circled one is drain....Fill till it starts to run out the fill hole.