You'll want to adjust your idle mixture also.  That's the screw on the right/starboard side of the carb (often hidden under a plug with a small hole in it, possibly with a dab of white paint on it).  That controls your low end.  You shouldn't need to change your pilot jet unless you can't adjust your idle mixture enough with the current pilot jet.  The white spacer adjusts the mid-range and the main jet will cover the top end.  The white spacer and idle mixture adjustments should reduce the backfiring considerably.  Please do some searches on this site and read the previous threads on backfiring and rejetting.  They are more thorough can I could hope to be and this topic has been covered very completely in previous threads.  Be sure to set the number of days to search back to something greater than the default of 7.  I usually use 500.  I'm personally happy with a 152.5 main jet.  So far as mileage, you'll just have to see.  Everyone's is different.

One of the nice things about a simple single cylinder engine is that you can put most anything on it.  For a stock engine the 36mm would be the best all-around performing carb.

The necessary details are:

- be sure the mounting flange is a perfect fit for the engine side of the carb.  If the stock one does not fit then replace it with one that does, so you have a perfect air tight fit.  

-Then you go to the throttle cable...will the stock cable work or does that need to be replaced as well.  If   repacement is necessary is there one on the shelf that will work or do you need a custom cable made.

-Other than  those issues, all you have to do is select an air filter and tune the carb.