Because you put BPCR in that list, I would say that the match to your Martini .22 would be a .38-50 Rem in a Highwall, a CPA or Ballard action.  The CPA being the cheapest probably.  It will be a decent Schuetzen caliber and a very workable BPCR caliber, it will shoot just about anything or anywhere you want.   

I don't actually own one so perhaps that just shows you how much I know, but for a one all around rifle, it would be hard to beat I think.  It would, however, be very limited to illegal in most Creedmoor style 1000 yds matches- but then that is not on your list either.   

Brent

to be honest the actions are really not that important.  The calibers are to some extent.  But you can win with a .45-70 in a Schuetzen match or with a .38-55 in a BPCR match.   

If you were going to have a different rifle for each, a .32-40 might be the most popular Schuetzen caliber.  A .45-70 is easily the most popular BPCR caliber.   

But the action should be what tickles your fancy.

Brent

Contenders are fine guns if you want to play with various calibers as a new barrel is fairly cheap. For a target gun, it is really at the bottom of the list. Now they are capable of fine accuracy, they have other traits that do not lend themselves to target work. One, being for benchrest you have to break the action open disturbing the fit to the rest/bags each time. Two, The weight is not sufficient for most people for offhand work. Three, the stock is more of a hunting design than a target design. Now I do like Contenders and can't remember when I have been without one. Currently I have a G2 in 30-30 throated for lead bullets and have a 22LR barrel that is currently being converted to a 297/250 Rook. Anything above a 30-30 case size is pushing it. I had a 45-70 Contender once and after three frame replacements I gave it up.

For rimfire, The BSA International Match rifle is a fine choice. I have an ISU and a Mk III and both are fine guns. For BPCR you have to have an outside hammer so a High Wall, CPA or Ballard can do. Caliber depends on what you like and if you are for or against case forming for some of the older cases. A 45-70 is hard to beat. Good accuracy and power and easy loading. If you plan on alot of Schuetzen shooting a 32-40 is pretty much the most popular. In a CPA, getting a second barrel is no big deal except for cost of course. The Win will be more costly for the take down feature and Ballard is pretty much dedicated to one caliber. 

Not sure this helps but good luck.

Well, 

As long as you are soliciting opinions. I think one could narrow things down to 2 rifles and you would be competitive in most of the matches. My choices would be those below.

1. Shiloh Sharps #1 Sporter, 30" heavyweight octagon barrel. Long Range MVA Buffalo Soule sight. .45-70 caliber. Finished to make NRA weight specs, and match the depth of your wallet.

2. CPA Stevens 44 1/2 with type 52 stock, chambered for .32-40 cal. #4 weight barrel 28" long with an extra barrel chambered for .22 LR also 28 " long #4 weight. MVA sights.

If I could only have two those would be the ones.

Bruce

Cost is a barrier to entry that's for sure. It's the primary deterrent to this sport.

I first got started with BPCS and the CPA in 38/55 but did not like the 3/4 prone aspect of that match and the fact it's a two man competition, without a good spotter you are handicapped. 

Changed it's butt stock to a Stevens 52 and switched to Schuetzen which compliments my modern rifle Silhouette shooting.  Then latter added another CPA with the Pope style high comb offhand stock in 32/40 & 22 LR.  Finally a bench rest dedicated # 5 barrel for the 52 stocked action.  I always say the rifles did not cost anything since I sold off assorted other guns to pay the bill. Did not do all of this on the same day. Has been a 15 year progression.

Keeping a rifle for BPCS and Black Powder Cartridge target doubles the expense since generally they don't shoot Schuetzen well and Schuetzens can't shoot there matches either.  Closest you can come is changing butt stocks on a 38/55 CPA but it's less than a ideal compromise.

I think I would see how committed you are to Schuetzen first with a single rifle and add barrels or if not  T/C's or CPA's three rifles that can switch between the three usual Schuetzen cartridges. .22 lr 32/40 and if using Black powder 38/55.   You can add as you go. In most matches around here you don't have to have Iron sights or Black powder out West it's another matter. One scope can do it all but tell you the truth I use 3 and enjoy using Irons at times.  My outfit is strictly traditional but competitive as well.

A Contender can shoot .22 Lr and one of the 32 cartridges using one scope for a fraction of the cost of getting traditional Schuetzens together. If competition is your objective, not staying traditional that may be the way to go. In a 9 lb rifle they can shoot as well as anything out there. Modern Silhouette is about 9 lbs sporter class and 10 Silhouette class and the best offhand work shot today is in Silhouette. While we like heavy guns Those rifles  would be very competitive in any offhand Schuetzen match. I don't shoot Schuetzen with mine but do campaign it Small bore Silhouette and practice on the ASSRA paper target. Scores are no different than my 14 lb hook butt plate palm rest high comb CPA. Have also shot my Schuetzen informally in Small bore Silhouette matches and same thing about the same knock down rate as the light gun.

Boats

I sorta agree with Bruce if you can afford 2 rifles. I don't know if a Shilo is a better choice then a Ballard or Hiwall for BPCR though. Like the others I also agree that the CPA is a good choice since you can shoot in the traditonal class in schuetzen and have multi barrels and even different stocks for BPCR. Another option would be to find a Stevens 44 1/2, although for BPCR you would be limited to .38-55 due to its barrel shank size and hammer clearance problem. Well, having thunk on it as I wrote, I personally would get an original Stevens 44 1/2 with .32-40 barrel for Schuetzen and either an original or maybe repro. Highwall or Repro. Ballard in .45-70 for your BPCR and Long Range shooting. Once you get "the bug" you won't be happy with just one or two rifles for long.

Sharps54, I am going to depart just a bit from the others on this thread so far and say that early on you will need a .22 single shot with good irons and scope both.  This will permit you to shoot in a variety of matches.  While my low-walls are a perennial and sentimental favorite, I think Martinis are hard to beat on a bang-for-the-buck basis.   

Second, I would look at a .38-55 in some configuration that could be used for both Schuetzen and BPCS... this could be accomplished with a special sporter style high-wall with both the crescent butt plate and the interchangeable small swiss.  I personally would want DSTs, but that is your call.  If I could afford/justify 3 rifles, I would "split" this second choice into a lighter recoiling .32 of some sort and an over-.40.  I went with a dedicated schuetzen high-wall in .32-40 and a BPCS high-wall in .45-70.  This is where the CPA or a take-down high-wall could come in since you could put both calibers on a single receiver.   

If you want to stay with BP loads only, an original or modern repro Maynard would be a possibility here as well, since they were world beaters as long as they were being made and factory supported with parts and barrels as needed.  I could see a single Model 1882 breech piece (receiver and stock) with a .32-35 barrel for schuetzen and a .40-60 or .40-70 barrel for BPCS.   

We can have a great bench session after the shooting is over at the June CSV match at Brushy Mtn.  Just one more reason to absolutely make sure you are there! 

Froggie