Briggs 28N777 on Coleman Vertex 7500 Generator

Go to Shop Parts and Equipment at the top of the page, click on Briggs then enter 28N777-the four digit type number. Most of your questions will be answered.

Scroll down to Popular Engine Manufacturers then click on Briggs parts, there is a link to Briggs parts look up

Beware that the IPL look-ups on Jack's can be only partials. A real pain for me but I learned to use other suppliers that have complete look-ups.
 
The only thing that comes in a kit engine rebuild wise would the gasket sets and carburetor rebuild kits. Other items must be ordered individually though most time you can order the piston with rings.
 
These are not bored but are honed to oversize using a rigid hone using the correct stones. Aluminum cylinders uses different stone than the cast iron/steel sleeved engines. Rigid hones take care of out round and taper cylinders, truing them back up. You also want to develop a nice 45 degree crosshatch so the rings will seat properly.
 
Personally I would not order parts until I know that the cylinder will clean up to the oversize and not over. I had some very close calls removing tapers. One I was down the last .001" before taper was removed. I also few that air pockets in the castings that made the over-sizing useless.

That one of the reasons I don't do many rebuilds either is the justification of replacement cost is exceeded. The only engines I have rebuilt is primary for myself though the ones I have rebuilt for customers carried a 90 day warranty on the work done. And one them they ran without oil during 100+F temps.