You should be excited.
First of all, the cut off number for low numbered Rock Island Springfields is 286,506, so you don't have to be concerned about the strength of the action. In fact, you have what is in my opinion the most desirable Springfield, the double heat treated model, which combines strength with surface hardness, making it just as smooth to operate as the case hardened actions.
The side mount is almost certainly a Jaeger. It is not a Griffin & Howe, Niedner or Noske, and if I remember correctly, the notches in the side of the dovetail base were the way Jadger locked the mount to the base.
The stock looks very much like a Sedgley. If it is, you will probably find his identifying mark of an"S" in a circle on the barrel. At any rate, it is a well done stock.
You should check the muzzle of the barrel for a star gauge mark at 6 o'clock.
I can't tell if the the scope has a 7/8" or a 1" tube, but either way you chould be able to replace it with a more weather proof scope, such as a Lyman Alaskan, if the former, and any modern straight tube scope, if the latter.
Here is a photo of a Sedgley belonging to me for comparison:\
