There are multiple connectors for the batteries on the market. Be careful of which type of connector you battery have and your ESC has. You might have to remove a specific connector and solder a new one on your batteries or your ESC. This is not a complicated task but you really have to be careful to not let the two wire of your battery touch each other. XT60 and Tplugs are the most common one and the one I use in this project.
The motors have almost always male bullet connectors and they should be compatible right away with the ESC’s female bullet connectors. The servo connector is used to connect the radio receiver to the ESC but also to connect the programmer and configure the different settings of the ESC.