Welcome to the forum. I would start by determining what your budget is first, and then whether your budget (or your desire) is for an original, or modern reproduction. Once you've determined which you want, and a price range, then the search begins. 
There are lots of gun shows around the country, and most of my collection came from these. Also keep perusing your local gun shops, especially those that handle the style of firearm you're looking for. Check the For Sale section here also, as there are some good guns there occasionally, at good prices.
If I was planning to use the gun for some target shooting, and occasional hunting, then I'd probably stick to something in a fairly common caliber. The .45-70 is a good choice, as is the .38-55. If you've not gotten set up for a fair amount of reloading, then an old gun or an odd caliber is definitely not in the equation. Most of these guns will require reloading your own due to limits on pressure levels, or lack of over the counter loaded ammo.
If you can give a little more info on your price range, and capabilities to reload, then might get a better idea of options.

An example of something I picked up a while back. 
Cimmarron high wall in 40-65 for about half price of new with tang sight. Modern reproduction if you want to go that way. Dies are easy to find and brass made from 45-70 is plentiful.   

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Good advice one size won't fit all.  Figure the end use first then select the rifle/cartridge 


Boats

I’ll give you the same advice that I give everyone who is just getting started in single shots. Get a CPA, set it up how you think you want it and start to shoot. In my experience almost no one ends up where the thought they would with their first rifle. The CPA has the ability to grow and change as you are pulled one way or the other. CPA’s take a back seat to none in the accuracy department and they are safe. 

40 Rod

How about a Trapdoor? Although a 45-70, a good original or H&R repro are at the top end of your budget and they are generally good shooters. Load it with the 405gr bullet & 55gr of 2F for 200/300yd and only need the heavier bullet/load for the long distances and hunting.

JSB30 wrote on Feb 5^th, 2014 at 10:40am:


That's the real issue with a Ruger #1. They are a very well built rifle, and nice looking too, but since they exempt the owner from some events, it wouldn't be my first choice. Better to start with something that wont restrict your choice of shooting events when you're just getting started, and don't know what you may want to shoot.

In my opinion 30" is a really good choice.  With apperture sights you get good sight radius and the benefit of having 0.01" on the rear sights being very close to 1 minute on the targets.  I have a couple of .38's with 28" barrels that feel better to me for offhand, but in the .45-70 it's nice to have the extra weight of those 2" of barrel.  I don't like longer than 32" personally, although I have a Shiloh in .45-70 with a 34" standard weight barrel.  I bought it used.  If I'd ordered it new, I would have picked a 30" heavy barrel.  34" barrels are a bit unwieldy.

Another factor is that some rifles won't make the legal weight limits with anything more than a 30" barrel.  A highwall can go with a longer barrel, and I imagine that a Stevens could too with no issue.   


Chris.