If you are going to be into long shots of 35 yards or more you will want to have HTL loads such as the Federal HW 3-1.5-#7s or 6s and in Hev 13 #7s,their #6s have not been that reliable for me.
Your threads are invector and some mfgrs do not make chokes for you commercially. HS Strut makes an Undertaker and Primos makes a Tight Wad. These chokes are under $25.
I like the Sumtoy choke for the Winchester . You can get very good results from H-13, Federal HW and Federal lead Flite Control in #5 and #6 shot ibn 20 gauge. Some more expensive chokes are the Pure Gold and Indian Creek. Someguns like the 555 constriction and others prefer the 570-575 .
Bear in mind that 20 gauges are much more fickle about what they shoot and don't shoot. At 30 yards I can shoot any lead load I want . At 35 yards I can shoot some lead loads. At 40 yards it just about has to be HTL .
At 30 yards most HTL give you a tight very dense pattern.
It will be about a month and I will be doing some extensive lead load shooting mostly FedFC and Win loads.