You are in luck! Your base is all or mostly there. The arm that has the threaded hole for the peep insert will be one of three standard lengths, yours should be the shortest, but longer ones can be cut to fit your needs.
The front sight should be a Lyman Globe No.17x, the x stands for Long, Medium, or Short. All three will fit and will work, but remember the taller the front sight the taller the rear sight. To see over the scope bases you may or may not need medium!
The No.17 Globe Sight uses inserts that are unique to Lyman, most other brands are way to large! There are companies that make "cards" of inserts for many brands, just make sure you get the Lyman diameter. A "card" has 10 or 12 different designs of posts and cross hairs. Some shooting sports require you use a specific one, others let you choose. Also the different "Thicknesses" are for different distances, just remember; "Finer is for further!"
I have a 2005 Winchester 1885 High-Wall in 38-55, the front dovetail is for the 17 Globe, and I use medium height, with the finest post insert. My rear sight is a modern Lyman copy of the Marble's tang sight (it uses O-rings instead of clicks to hold the adjustments in place. Your rear sight is much better and far more accurate! For a quick lesson on how to read and use the scales on the receiver sights go to Montana Vintage Arms web sight. Your scale may or may not be a little different, but the system is the same as reading a slide rule (That's why most of us need a quick lesson on how to read them!) Most current 22 competitions are at 50 & 100 yards or meters, but in the 60's and before they did 200 yard also, and a few clubs went all the way to 300 yards! This type of shooting will dictate your height needs for the rear sight.
MVA also makes high quality reproduction Winchester scopes and mounts for the external adjusted scopes. They may be able to help get you scope system up and running. Just remember: All it takes is MONEY! If it is Unertl there is help out there. If however it is Lyman or Lechner (sp), you are on your own, (I use a great big Unertl 15x 2" for my old eyes!)
Have fun! You can PM me if you have questions.
Ivan