Question

You will get about as many different answers as responders to that question.  I believe that many people who shoot the plainbase matches own heirloom antique rifles and are already involved in the ASSRA Scheutzen events and wish to compete with the toys they own.  A noble endeavor.

My own feeling is that a rimmed case that is plentiful, in current production, and of common, standard caliber is best. You don't need an antique or special optimized wildcat cartridge.

Indeed, I was not the recipient of fine old single-shots, but wanted several, so had my own purpose-built because I could not find what I wanted.  Later I got lucky and found several lovely old English rook and rabbit rifles which I had restored and I kept one I had relined to .32 S&W Long and gifted the other, a .360 No. 5 rechambered to .38 Special Wadcutter to a friend.

I had built several single-shot rifles using small pre-WW2 H&R .410 and 28-ga. frames, in a variety of calibers. Because these are not particularly strong actions I shoot only plainbased cast bullets in standard pistol calibers and currently have several rifles each in .32 S&W Long, .38 Special, .44-40, and .45 Colt. I have two modern .44 Magnum single-shots, one on H&R SB2 frame, and the other on a Beretta 412.

These ALL work for recreational and hunting purposes. All except for the modern SB2 are light-weight woods and walking rifles, not shot in matches.  With iron sights the prewar H&R .44/410 frames in .32 S&W Long and .44-40s weigh only 4 pounds, the similar era 28-ga.frame .38 Special and .45 Colt rifles 5 pounds.  The Beretta 412 .44 Magnum with 28" tapered barrel weighs only 6 pounds and carries like a somewhat heavy, but balanced fly rod.

The modern H&R SB2 with 20" bull barrel was 7-1/2 pounds, too chunky and heavy to carry around in the woods all day, so I sold it.   

My preferred walking guns are all LIGHT.  

The 4-pound .44-40 is my favorite with either bullet, round ball or shot, black or smokeless, doesn't care!

Any of these will shoot 3-inch, ten-shot, 100-yard groups with my cast bullet loads and iron sights.  Maybe not competition quality, but they ring the gong consistently, are fun to shoot and bring home lots of game during the appropriate season. Best of all they don't beat you to death, except for the folding action  Beretta .44 Magnum when shooting full loads! That's what the leather covered recoil pad is for.

I like to use a bullet which is somewhat heavy for the caliber, using soft alloy, typically 8-10 BHN tin-lead, with a caseful of powder which produces the desired velocity with safe pressures using a slightly compressed charge of powder and which provides base support for the bullet so that it may be firmly pressed against the origin of rifling upon breech closure, without the bullet telescoping back into the case.

In the .32 S&W Long I use a Accurate 31-155D with a case full of 4198 or RL7 in a ten-inch twist barrel.

In the .38 Special I use Accurate 36-245D with a case full of 4198 or RL7 in a 16-inch twist barrel

In the .44-40 I use a Accurate 43-230G or 433-230EB and a case full of 4198, RL7 or 3Fg Goex in a 36-inch twist barrel.

In the .44 Magnum I use Accurate 43-230EB or 43-260C and a case full of 4198 or 3Fg Goex in a 20-inch twist barrel.

In the .45 Colt I use Accurate 45-259EB or 45-290H and a case full of 4198 or 3Fg Goex in a 20-inch twist barrel.  

Perhaps you recognize a "formula" here...  John Taylor built them all for me over about a 10-year period.