The stock F36 uses the square 1S LiPos with a pigtail on the battery and there are no upgraded batteries in that format. You're going to want to switch over to tinywhoop style stick batteries. These do not fit in the stock F36 frame. You'll have to cut out some plastic in the frame's battery tray to make them fit. Some people even use foam to make sure they fit snugly.
You don't even have to desolder the original connector if you don't want to. Just solder on the new pigtail's positive and negative wires to the topside of the flight controller, where the original battery connector is. The black (negative) and red (positive) connections on the right side of this image:
http://www.quadcopterpatrol.com/wp-content/uploads/2017/01/furibee-f36-circuit.jpg
Here's an example of the tinywhoop style stick batteries (with a JST-PH 2.0 connector):
https://www.amazon.com/Crazepony-230mAh-Battery-Inductrix-Connector/dp/B01N0Z0ME2A
A lot of people say the GNB branded ones are the best performance. I was just sharing this Crazepony listing because it has the connector you need included.

These are the standard sized batteries all tiny whoops use, so if you ever upgrade, these style of batteries will be good. Do you already have a charger for 1S LiPos?