We had what we thought was a perfectly good kohler toilet... never any problems... then one day it simply stopped flushing properly. Thought it was just a clog... plunged... sometimes it goes down, sometimes not.

Checked valve and flapper and tubes and ballcock. Replaced flapper (it was an old black one)... still sometimes down, sometimes not.

Siphon action looks good at start, then sometimes bowl fills, sometimes not.

Pulled toilet off completely, snaked and snaked and snaked., doesn't appear to be a clog... water runs freely.

Big question: based on budget...which comes first: the plumber or a new toilet?

Thanks so much for any advice... willing to do anything and everything to get up and running... but would like to proceed based on good information!

which comes first: the plumber or a new toilet?

Plumber.

Could be a defective fill valve

OR

Could be a blocked vent pipe.