Depends what size generator.  There are manufacture recommendations included in the owner's manual.
Note:  cca = cold cranking amps


Generac Air Cooled Battery Size Recommendations:
These are automotive type batteries, always refer to your owner's manual for specific information.
• 8 kW: Group 26R, 12 Volt, 350cca minimum
• 10-20 kW: Group 26R, 12 Volt, 525cca minimum


Briggs & Stratton Home Generator Battery Information:
Note: Do NOT use an automotive type battery.  All batteries are 12 volt DC and must be valve regulated lead acid type.

If Your B&S Model Requires 33 Amp Hour (Vertical)
Recommend: 12 Volt DC, 350 cca, AGM (Absorbed Glass Mat), Terminal Hardware M8, Dimensions (Inches): 5.32W x 7.87L x 6.87H.
Werker Brand p/n WKA12-33C, SBS p/n S-12330

If Your B&S Model Requires 50 Amp Hour (Horizontal)
Recommend: 12 Volt DC, 600 cca, AGM (Absorbed Glass Mat), Terminal Hardware M6, Dimensions (Inches): 5.5W x 9.0L x 8.25H. 
Werker Brand p/n WKA12-55C/FR, SBS Brand p/n MH19767, Vision Brand p/n MH25860

If Your B&S Model Requires 55 Amp Hour (Liquid Cooled)
Recommend: 12 Volt DC, 650 cca, VRLA (Valve Regulated Lead Acid), must have top posts, Dimensions (Inches) 7.5W x 7.25L x 10H (including posts). 
Werker Brand p/n WKDC12-80P