I would guess a model 1893, or an early model 1894. Not enough pictures to determine caliber.
I will note though, this gun has been heavily modified. The buttstock has been straight cut and a pad added. The octagon barrel has the sharp areas rounded. The wood has been refinished, and the metal has been reblued. Additionally, the reciever has been drilled and tapped, which is not factory done on a levergun of this vintage. Whatever collectors value it may have had is now ruined.
The only monetary value it has would be as a "shooter". And believe it, or not, in today's crazy levergun market, it could possibly bring $600 - $700 ).
As for caliber, if it hasn't been rechambered, it's likely a .32-20, or 44-40. Outside chance it might be a .38-40. The markings on the barrel should indicate original caliber.
In any case, with a gun that has been reworked as much as this one, you should have a Gunsmith check it over, and have a chamber cast performed to determine caliber.
How about a pick of the other side. And one of the top a little further down the barrel from the receiver. We should be able to see the caliber. In other words between the rear sight and where the barrel enters the receiver.