I would suggest a 32/40. You can get anything you want for it "off the shelf". I would start with a 14 twist. 

This is a good, resent thread on BSing:

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further, the .32-40 is thrifty to shoot. a miser at burning powder, brass lasts forever and the fussiness of many cartridges is absent for the most part. I have been shooting the same one for nearly forty years and still have some of the brass I started with. For what it's worth.

Tom, the guys above are talking about 32-40 not 32-20, but maybe you just entered the wrong number.  The two are different animals.  Brass can be found for either, just need to be patient and keep looking.
Bob

Dr. J,
If you go with a modern built/ rebuilt rifle in 32-40, you will need a good bullet mould, a way to lubricate your bullets, a breech seating tool, a re- and decapper, and a powder measure.  A box of 20 fresh cases will be the greatest of plenty brass, since you will probably use the same one over and over.
It may seem a little daunting to begin with, but if you compare it with the cost of a good set of golf clubs, or a skiing outfit, or whatever equipment intensive game you look at, it becomes reasonable!
Of course I’m an infamous enabler and you’ll spend the rest of your life chasing “the next best thing” but I’d love to give you a little shove at the top of the hill!
Good luck!
Froggie

In a pinch just use 30/30 brass and neck it up or fireform it.  Are you planning on using a plugged case to seat the bullet?  If so, you might as well have CPA make you one or maybe two, one to start into the barrel and the other to seat it to the desired depth.  I learned that trick from Gail's father Paul when looking to breech seat my 25/35 Original Stevens.  I have to use a tapered bullet with a plugged case.  When I breech seat in my 32-40 built on a Story Striker I use a mechanical seater and can shoot any alloy or bullet but still use a tapered bullet.  I don't have a measure suitable to use at the range so I measure all my charges at home and put them into plastic vials with rubber stoppers like they use when they take a blood sample.  They are easy to find and fit into a plastic 50 round cartridge box.  Have fun.  Tom

I have 4 32-40s, one Ballard and 3 high walls.  Short cases like the 32 RKS might give you a slight competitive advantage they are a pita because they need a wad.  I am a fan of NOT precharging cases and prefer having a powder measure on the bench. I have adjusted charge weights in the middle of a match to address vertical stringing.  You can use a wad material like thin sheets of floral foam for at the bench loading but the 32-40 doesn’t need a wad and had shot many a 250. 

Jack

My question(s) now pertain to bullets and bullet molds. I’ve never cast  before, are some bullet shapes easier to cast than others? Which bullets work you suggest, what mold makers would you recommend? 
I was given a 20lb. Lyman pot and ladle, are these adequate to start with? Metal composition 20:1? Am I somewhat in the ballpark? My apologies for all the questions,  but I’m obviously green as the grass when it comes to this subject. Thanks, Tom