Own both a Stevens Favorite and a Stevens model 44. They are kinda similar in appearance. Do believe Stevens shown, is a model 44 Ideal. Heavy round/octagon barrel on it gives it away. Favorite is kinda a kids rifle and will not have that barrel. The 44 is a much larger rifle and was chambered in nine cartridges, anything from a 22 LR to the 44-40 and yes, 25 rimfire too. By the way, Stevens didn't make the 38-55 and 44-40 ones too long. Seems the action loosened up too much with those rounds. Also, if it were a Favorite, should have that name stamped into top of the receiver. Leastways, mine does.
My 9 year old Gun Trader's Guide catalog shows the value of one in good condition to be $425. Think I paid around $250 for my 22 LR model 44 about 5 years ago and it needed some work.
Now if it was a 44.5 Ideal, Stevens changed the action some, making it stronger, you can double the value on it.