The No. 1 also has a barrel rib for scope mounting.
If you want to work the existing stock then either one can be turned into an interesting custom depending on what you like. The No.1 can be very elegant but the No. 3 can be made up into a very trim little rifle as well. The No. 3's
generally had much plainer wood back when Ruger was putting decent wood on their No. 1. Nowadays the wood in No. 1's isn't much to write home about anyway. If you want to restock with new blanks then the sky's the limit on how fancy you can go, Then it would be more a matter of which lever style you like and whether or not you want a quarter rib - although even that can be removed if desired.
Can't display the pics directly here since they are proprietary to his site but this guy reworks both models into very nice designs, either by modifying the factory stocks and leaving the barreled actions alone or he can strip out everything but the receiver and start from there.
Check out the No. 3 about halfway down.
No. 1 and No. 3 reworkedHere's a No. 1 completely redone with a new barrel and removing the rib.