I recently acquired the Schuetzen stocked highwall bought from Joe here on the forum. As usual, his add gave a perfect description of its condition. It’s a handsome rifle and I’m very pleased with it. I’ve refit the stock and made a couple minor repairs and it’s now ready to be shot.
My only experience with the 32-40 has been with fixed ammo in a Model 94. I sold my dies with that rifle so I’ve ordered a new set. I have plenty of new 38-55 brass so I’m hoping to form a few cases from that. A friend is bringing me some breach seat bullets to our last bpcr match this weekend. I have a pound of AA#9 powder which I’ve read is acceptable. 
My goal is to see if it has any potential for accuracy. Joe described the bore as good and it is. Good but not excellent. 
I have no experience with breech seating and am hoping for any advice on how to proceed without committing substantial investment and using what I have on hand. 
The results will determine what I’ll do with the rifle. Your thoughts are appreciated.
JKR 

I'm not a breech seater but I think that you will do better using 32 Win Special brass to form your cases. One pass through the sizing die and your done.

The biggest issue for accuracy is consistency. The correct bullet is essential as well. My DST 32-40 that I bought last year at the Post Falls show with a 16 twist barrel ended up liking a Hoch bullet that weighs in about 185 gr but only in 30-1 instead of my usual smokeless 20-1. The new Pope 32-40 with its gain twist barrel lik d my go to Borton/Darr 3 groove bullet in 20-1. 
Experimenting with breech seating depths can tighten up groups as well. While a fixed depth push seater can work it is desirable to have a seater that can be adjusted. There are lots of variables and fiddling with them is part of the fun. My match rifle stopped shooting well a couple of years back but last spring I was experimenting with velocity changes and powder and found the using Accurate 4100 and increasing my velocity from 1440 to around 1490 shrunk my groups back to the 1+” range at 200 yds. Just an example of what worked for me. I have the benefit of having several of my high wall breech seaters that had flaws that prevented me from selling them but that didn’t affect functionally available set to different depths so I can experiment without having to make adjustments. With 5 32-40 high walls I use different depths with different rifles. 
Good luck in your journey. 
Jack

my ol' rifle, original Winchester 16:1 twist, is fond of bullets between 180-195 grain. The best is the old Ideal 319289, but others have done well. Tapered slugs are seated with a Webber seater.
Powder is almost always 4227, but my dwindling supply of 4759  works nice too. Primers are Federal 210m and some Winchester WLR. All simple, all traditional and long proven in my rifle and about a jillion of others as well. Cases last a long, long time at the pressures it operates at. 
Now and then I go in another direction with powder or bullets but soon come back to the recipe above. 
I do envy you that rifle, it has all the earmarks of a damn good one and handsome to boot. You are gonna love it.