Perfectly good old engine, except...

Hi everyone. I'm sure this has been asked, but if someone would kindly direct me to a blog, forum thread or other, I would be grateful. I just can't find the right search term. I have an old generator (Powermate 6500) that was kept indoors and only used during rare power outages. How do I go about finding a rebuild kit for the carburetor that doesn't seem to be available anymore?
 
I am not a mechanic, but I do know my way around the basic engine and can replace just about any part. I find it incredibly difficult to find parts as most of my powered equipment gets used infrequently, sees little use and by the time something needs to be repaired, parts are no longer available (or they're crazy expensive, more than the machine is worth). Carbs, in particular. From my perspective, there are a gazillion different carbs, none of them with identifiable marks, often interchangeable jets for customizing to specific engines and they become obsolete very quickly. Are they more standardized than I perceive?  Is it possible to determine fuel flow/jet size based on engine HP where one can find a suitable off-the-shelf replacement? I really hate buying a new generator every 5 or 6 years just because the carb is gunked up and parts are no longer available.
 
BTW, the generator in question has a cut-off valve that I used every time and then ran the bowl dry. What little fuel is in the tank was bad and I know better than to try to start it using varnish for fuel.  Still, the amount of debris in the bowl is crazy. And, I only use pure gas. No ethanol.
 
I appreciate the help!

First, post the make and MODEL # of the engine itself.
 
I do a bunch of generator carbs (SW Florida) as they sit between hurricanes and only come out of "storage" not to start (due to old fuel).
 
Easily, 95% of them I can get running W/O any parts.
Really bad carbs, I'll put in the Ultra Sonic machine.
 
Briggs for instance, their float needle seat (a softish rubber?), may be the 
biggest "leaker" of fuel and not sealing.  You can buy a full set of the red 
seats on Flea Bay for cheap.  Those are easily changed and I've had good success
with them.
 
I would try to keep away from aftermarket carbs and repair what you have. 
Flea Bay carbs are a 50 / 50 shot at fitting and even working correctly .
 
I also mainly use brake cleaner on the carb where rubber may be.  Carb cleaner is somewhat harsh and will often ruin any rubber seals.
 
With a model #, you can look up the engine, look up the carb and then find what parts you may need.
With just a part #, enter that and do a search..  It's rare I can't find a part needed.
 
Your sized generator probably has a 10 HP Briggs (super popular, I own 3). Carb and carb parts
are easily found.  
 
I would do a tear down and a good cleaning.  You'll very likely be able to save it with little to no parts...
 
.