On my previous Onan 5500 I would prime it for a couple a seconds, crank and prime again and it would start. This would be if it had sit for a couple of weeks. Once it had been running, it could be restarted with no prime up to a day or two later. Not sure why there would be a delay when starting, I never experienced that.
One thing I would highly recommend is to install a simple inline shut-off valve in the fuel line (if your fuel is gas) and always turn the fuel off and let it run until it shuts off. This is really important if you don't run the genset regularly, otherwise the gas in the carburator will probably gum up and cause issues. Also make sure you add Stabil fuel additive to the gas, this will help prevent the fuel from deteriating after setting for real long periods of time.
2015 Pinnacle 36FBTS
2015 F250 SD Platinum 4x4 - 6.7L PSD :
Titan 50 Gal. Fuel Tank
Slotted and Dimpled Brake Rotors
Air Lift LoadLifter 5000 Ultimate Airbags with WirelessAIR Controller