Congrats on your new purchase. I am sure you made a good deal for the price. A couple of responses to your original questions.
Any contender barrel should fit on your frame. Encore barrels will not, but any contender barrel will.
New contenders have two locking lugs on the barrel. Older contender barrels have a single locking lug. When you break the action open, the locking lug is the thingybopper sticking out under the chamber and rubbing against the face of your frame. If it is a two piece lug, you should be able to see the line between the two pieces at the apex of the "U" in the lug.
This next question, for me, is a no brainer. For someone new to contenders, it may be a tough decision. If your frame is one of the older models, you can send it into T/C and they can upgrade it for you. If you send the barrel in with it, they will fit that barrel to your frame so it fits perfectly. If this were my gun, and it was the older model, and it had a single locking lug on the barrel, and I really really wanted to hunt elk with it next year, I would be sending it off to T/C for the upgrade and to check it out. When you get the gun back, per some purists, you gun will have less "collector" $$ value because it is no longer an original T/C. Per the hunters in the group, you will have a more reliable and likely more accurate hunting machine.
If you are hunting with open sights, go shoot a few silhouette matches and see where that gun is hitting at 50, 100, 150, and 200 meters. Then when time to go hunting, it only takes a second to set your sight based upon the shot distance in the area you are hunting.
Good luck and enjoy that new T/C.
Steve