Expect a thousand different answers to this question, as "best" turkey gun is largely a matter of personal taste. Similar to asking someone what their favorite dessert is.
For me a couple come to mind:
Remington 870 3.5" supermag with the Sure-Shot stock, Primos Jelly head or Indian Creek 660 or 665
Mossberg 835 with a Star Dot .676, Rhino or Indian Creek