...try to separate the hot and cold airflows.
tThe engine is probably air cooled so that will have a fan blowing over the cylinder so my vote is for suck
Possibly make the hot able to be redirected for a bit of free heating in the winter.
If the enclosure is fairly well sealed, Blow! try to keep positive pressure.in enclosure
Is it air or water cooled ducting is good if it is water so flow is directed cold air in to unit fan\radiator then duct to outlet
Just remembered, few years ago I looked at ventilation issues on land fill gas engines at the land fill site in Brogborough, near Bedford
They have shipping containers fitted out with engines / generators.
I don't know the size of your generator but it probably wont be a bad idea to see how they do it.
Get it wrong and your issue could be build up of carbon monoxide
It's a hotly contested topic with PC builders/gamers, I believe a "through flow" with an inlet and outlet fan is considered best, positive pressure is good and negative is worse as it draws dust in through any gaps in the case, I'm sure Linus has done a video on it.
Exhaust would be piped out.
To far to move hot air to the house.
Water cooled in a silent type enclosure that has defined air flow paths.
Probably wouldn't want "stale" enginey air indoors anyway.
Then most of the work is done for you, duct the outflows out of the building and put an inlet into the building somewhere else. Inlet low down, outlet higher if possible. You may need to go into the enclosure and double check for potential recirculation paths.
Check engine temps before and after. You probably won't need any additional fans if you've got good, non resistive ducting.