Burner the only maintenance I do is clean the coils every month or so. I run lots of heat and I find these tend have large amounts of scale buildup if I don't keep on top of it.
I have a vacuum gauge between the pump and filter to let me know when it is getting full. I carry a spare filter, thermostat, and flow switch for the burner in case something breaks in the field.
Engine I do oil changes when I get a chance, I have had a few times it has got up to 200-250 hours or 3-4 weeks. I use synthetic and the long life oil filters, engine is a briggs with 3000 hours on it. I still have the original secondary air filter in there, but have replaced the primary a couple times. I think I am up to my third set of spark plugs, and probably a half dozen fuel filters. Only thing I have had to do to this engine besides what is listed above is add another fuel pump as the factory one had a few issues. Engine is a big block 35 hp briggs, seems way better built then the 2 smaller red briggs I have.
Quick connects, I will change o rings when needed, although if they start giving me issues with coupling I just replace. Same thing with guns and other throw aways. I would fix and maintain these, but I am way too busy to worry or deal with this. 1 hour to pull apart and replace what is needed in a gun, I make enough to get 3 new guns. I would rather spend time with the family then monkey around with throw away items.