In the old days, the .38-55 was technically the more accurate caliber, and many early benchrest matches were won with it.  The .32-40 was more wind-sensitive and critical in loading, hence less technically accurate, but the reduced recoil made for less fatigue and better scores in offhand shooting.

Nowadays, the more precise machining of barrels and moulds, and the use of smokeless powder means that variables that used to need more weight and diameter to reduce effect aren’t there so much any more.  A good .32-40, with a good shot, probably wouldn’t be giving anything up but recoil and expense.  Now it’s the .28-30 and .25-20 that are slowly closing in, with even less recoil fatigue, if you can load them right.

By Schuetzen, whether you are asking about a cast bullet rifle to shoot offhand or bench rest, the answer is the .32-40. You can't go wrong with that caliber. While the .38-55 is inherently an accurate cartridge, nearly all the current accuracy records are held by .32 caliber rifle shooters. The .32-40 also recoils less and that is no small matter, especially if you intend to shoot in matches.
J Louis' statement about the .33-47 has merit but due to it's not being main-stream (in the Schuetzen world) may be a little too much to deal with for a first rifle.
If you plan to shoot fixed ammunition or breech seat are matters of concern but can be dealt with once you make a rifle choice.
Good luck on making your rifle choice and welcome to Schuetzen.

I would also not count out the 25's these days as one would also have a rifle for the 25 Caliber matches as well. I have been shooting a 25-35 and it hasn't taken a back seat to any of the various 32's. Also extremely easy to get to shoot and also allot more pleasant / fun to shoot off of the bench. I have also chambered the same for others in our group. Below are just a couple of 200 yard targets being shot and also have quite a few more of the same I can share. Barrels are 10 twist and the bullet being used is the Mos 120 grain Spitzer. These two were shot by a couple of the folks in our group and the first one from a new shooter to the Schuetzen sport. And this is still only his first year of Schuetzen competitive benchrest shooting. The increased velocity of the 25-35 over the 32-40 makes the wind drift very similar to being the same as the 32-40. 

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That second target was shot by Jack Hughes on this site. I have chambered four for friends, Jerry Hartwig one and I just sold my 25-35 chambering reamer to Jerry Cleave who is going to build one for himself. Below is a picture of my practice 200 yard Iron / Tube Sight target that I shot. 


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Where are matches held here in PNW?

Go to a local match and most will go out of their way to help you out.
The exception being those who always want to finish at the top. 
And those unfortunately are not what I think the Sport is all about but it is about bringing everyone to a higher level of competition.

Mr Wright's various books are very informative, extremely well written and have a lot of data as well. While I do not have a rifle for the Schuetzen game I enjoy reading them and have done so multiple times. I do shoot cast bullets in some of my mil surp rifles though. Frank