If you are looking to keep weight and profile down I would look at Warne RF rings, no rail required.
For that scope I would advise the MilDot version though it does not have illumination if you can do without there.
That BDC isn't going to jive well with 22Lr at all. Also realize the Talos is Second Focal Plane and reticle is only valid at 10 power.
If you can swing it the TalosBTR 4-14x44 is a great scope for 22lr. It is MRAD based, has a nice reticle and is illuminated.
This guy is FFP so reticle is valid at all power ranges.
If you do any early morning or late evening hunting, you know how important a low light accurate scope is. Try our Talos line of riflescopes.
athlonoptics.com
Ring for it would be
https://warnescopemounts.com/product/warne-30mm-rimfire-high-matte-rings/
If you want to keep to the Talos line and need illumination I would look at the 6-24x50 ATMR1
Shooting in the early morning and late evening light are no problem with our Talos line of rifle scopes. Optimized for low light hunting scope performance.
athlonoptics.com
It is Mil based and has a good reticle.
You are going to be holding ~8 Mil @200yrds in 22LR Sub (1080fps) so you want a reticle that can give you what you need for distance you will be shooting out to.