old ethanol gas can do bad things to a fuel system, and even after replacing a carbruetor, the old fuel in the tank and lines will carry debris into the new carb.
the fix is to run some seafoam fuel additive thru it.... it will quickly dissolve the built up gum and varnish that ethanol fuels develop so quickly when it sets.
if you know how much fuel is in the tank, add the correct amount of seafoam (2-3 oz per gallon of gas) and then run the motor long enough to insure the seafoam gets into the carb.... let it set overnight and start and run an hour or more the next day.... it will burn out all the dissolved gunk and fix the problem. any bad ethanol fuel that is left in the tank is treated, and adding fresh fuel should allow it to easily pass thru the system without a problem.
a filter is ALWAYS a requirement, but Ive never had a fuel shut-off inline of any genset Ive ever owned, and have never had a problem as the fuel set in the carb over the winter.... if its going to be a long winter, using the blue stabil will help a lot (red stabil does not work on ethanol fuels)
but the very best thing one can do to prevent bad fuel, and dirty/damaged carbs, is to use ethanol FREE fuel. you will never again have an issue unless you get a dose of dirty fuel...
and all the other small engines I have that DO have fuel shut-offs, I dont shut the fuel off.... still no problems... using clean fuel in a clean system is the only way to keep the seasonal maintenance to a bare minimum..