32-40 is what I think the general consensus will be with the following ( I list an order so others can suggest improvements):
1) CPA is a fine choice but get the fast lock time and lowered hammer for easier breach seating tool design.
2) 28" #3 weight barrel unless you are young and strong.
3) Schuetzen lever ( although I prefer the loop).
4) High comb stock 
5) Single prong schoyen plate.
6) 14 ± 2 power Unertl 1 1/4 or 1 1/2  or lyman super targetspot.
7) Iron sights are up to you (MVA Soule or others)
8) Bullet mold I would go 190 ±10 gr
9) 1:14 ish twist.

Let the fun begin,
Charles

Gard72977
bohemianway presented a good set of parameters for a first Schuetzen rifle. As one who has been in this game for several decades I agree that a CPA can be a good way to get going. I suggest you consider not getting an exaggerated high comb buttstock though. The No.52 Stevens would be a better choice for starters. It's not difficult to manage for bench rest shooting yet is a good for offhand also. If a high comb buttstock does not properly fit you, it will not be comfortable to shoot. I'm not a fan of the single prong butt plates but it's a matter of personal choice. The "Schuetzen" lever is, I assume the 3-finger lever and is a good option. Consider also the loop and spur lever, especially with a wood filler in the loop.
A 32-40, 28 inch, 1:14 twist, No.3 weight barrel is another good choice. 30-Inch length works well too. Consider a full round, no taper contour. Another good barrel contour is full octagon. You will be happy with either. A 190-200 grain bullet is another good recommendation of bohemianway's. Consider a spitzer, cast 1:20 and push it at about 1425 feet per second so it will stay supersonic out to 200 yards.
Scopes are a whole discussion unto themselves. 
You state you are an offhand shooter and practice a lot, that's great! Use as high power scope as you can get your hands on. Some of the best shooters in this game, from the 1980s through today have used 36X and even more for offhand, so consider a 20X if you can find one. You can choose either an older Unertl or Lyman external adjustment or go with a more modern internal adjustment scope, your call.
Take your time to plan out a rifle by making a list of what you want to do with it. Will it be strictly and offhand rifle or will you also shoot bench rest with it for example.
One last point. While the CPA is a good choice, it is by no means your only choice.
Welcome to the Schuetzen game and I wish you the best in your shooting endeavors.

When I say I practice a lot I mean with a hand gun. The Schuetzen will be a offhand only gun for me. The pistol gets to be more like work than fun. I want the rifle to just enjoy shooting. 
CPA seems like a good way to get started. I have been looking on gun broker and there are a lot of nice  original 8.15x45 German guns. I need to sell several guns to generate money. I'm just starting research for what I want.

I appreciate the time people take to respond.

My suggestions would be:

32/40 caliber

14 twist, #4 straight octagon barrel, at least 26" long. #4 straight round, second choice, they are a little cheaper and lighter.

The available NOE copy of the Paul Jones type bullet.    (You need to Login or Register to view media files and links)

Lyman and Unertl scopes are common in 20X, 3/4" Unertl are more expensive but, are not superior to the Lyman's. Higher powder over 20X bring a premium for price for both. 1" Unertl's are much more expensive than 3/4" but, a little better optics and more FOV. Buy what you can afford. Good modern scopes are also a good choice (Weaver the best bang for the buck).

Frank

I've only held a couple of schuetzen rifles and I came away with this:  The exaggerated shapes schuetzen stocks are very personal  Try some out before you buy.

As this is your first Schuetzen get a 32-40 there is a boatload of good information on shooting a 32-40. Get a Douglas or Shilen 28” #3 barrel with a 1 : 14” twist, then ask Paul to recommend you a bullet mold he will steer you right. 
Personally I have never liked a high comb stock I’ve never been able to get my face on them right. I’ll second the #52 stock. 
The 32-40 is no slouch it will keep up with and of the modern high-pressure .357 based cartridges and it is a lot easier to get going. After you master the 32-40 you can have Paul cut you a barrel for something else if you want but I’ll bet for offhand you’ll stick with the 32-40.

40 Rod 

I would not over look the 33-47 it is extremly user friendly and extremly accurate. The 234 grain bullet is a little more forgiving in the conditions and the recoil is similar to the 32-40. Bullet moulds might be a little harder to come by but it will give you a little more than the 32-40 has to offer especialy for a new shooter. Hopefully Terry Harper will chime in with his opioion and success as being a new shooter it being his choice as he has and continues to do extremly well with his from day one. He also chose the CPA and he give you all the specifics of his rifle.

JLouis