Whatever you decide stick with a 20 gauge using TSS ammo. It kills plenty good enough and doesn't knock the snot out of you when you pull the trigger. Good luck on your choice.
My only caution against TSS besides being over $10-$15 a round is availability.
I went into my local BP and Cabela's 3-4x a week prior to turkey season and looked on line daily and had great difficulty finding lead Winchester Long beard XR Turkey shells and TSS and when I did find TSS in stock it was WELL over $13 a round.
Neither my local Cabela's or BP had any 20ga TSS in stock until a few weeks prior to the opening of turkey season and only 12ga TSS for $13-$15 a round.
Based on my LIMITED experience with TSS and what I have read here and at the two most popular dedicated turkey hunting websites TSS is often picky as to what choke it will perform well with and often doesn't pattern well with the same tight chokes used for lead turkey shells most guys already have or come with new turkey specific guns, so patterning your gun to get optimal performance from TSS shells could be vary costly and if you need to buy an AM TSS compatible choke it can get down right painfully expensive.
And if you're going to limit your shots to 45 yards or under there is no need to use TSS as lead will do fine at 45 and under.
I would respectfully suggest you do some lengthy research of TSS turkey shell before you invest any $$$ in them or TSS compatible chokes. Another issue related to TSS cost is they are so expensive it can become for some hunters cost prohibitive to stock pile multiple seasons worth of shells and with the current ammo shortages especially with season specific limited run turkey shells like TSS and WLBXR's, you could find yourself two weeks away from your hunt and either have only a few TSS shells or none at all.
I literally have stockpiled 10 turkey seasons worth of Winchester Long beard shells for my sons and I and thank God I did as they never were for sale OTC near me and only available on line and if you weren't among the first to find them you didn't get any. Shockingly enough the best source for reasonably priced WLBXR shells was of all places Gunbroker.
Just some things to think about before you go all in on TSS.