grizzly hit the nail right on the head trkytrcks,
based on the info you've given , the handmedown gun you are using could be called a GENERAL PURPOSE gun. that may be one thing to consider when purchasing a new one . will it be solely for turkeys ? or will it be used for deer, pheasants, and more?
the Rem. 870 express and mossberg 835 pump or mossberg 935 autoloader are excellent choices. either of these can be bought with a single barrel or combo . of course the combo is more money .
either way you should consider what it will be used for . if it is to be used as a general purpose arm you should go for the 26 or 28 inch barrel , as it will handle and swing much better than a short one . also , if it a GP gun, stay with the traditional style in stocks vs. the thumbhole style. the thumbhole style is alright for turkey and possibly deer, but for swing shooting upland birds it may be a handicap. good luck and congratulations on your first year success.