The M81/82 scopes were used until 1945 when the M84 was adopted. They were the only "issued" scopes for the M1C/D's however non-issue scopes were used, that being the Stith-Kollmorgan 4X or the Lyman Alaskan.
Anything else would be just a scope attached to a M1, which is fine, just not authentic if authentic is what you're looking for.
There are a lot of re-productions out there, some good, some not so good. Prices will vary depending on the quality. There are original scopes out there, but as mentioned they can be pricy depending on the condition.
The only one I used was the M84, I ran sniper schools for the Guard using M1C/Ds with the M84. They are 2.2 X but worked great to 900 yards.
To get an ideal of the best after market scopes check with the guys on the CMP forums. They have gotten quite popular in the last few years do to the CMP GSM Vintage Sniper Matches.
Because of the (lack of) quality of the after market M1 scopes, and the high prices of the originals, M1C/Ds don't fair well in these matches compared to the M1903a4's and the M1941s. There are a lot more "original" scopes available for those rifles.
But if you're willing to pay the price for a good original M84, and learn to shoot the M1C/D they will be competitive.
You only shoot the Vintage Sniper Matches at 300 & 600 yards. One of the best M1D shooters I've seen put a cheap after market M84 and never got it sighted in. He just hung the scope on the rifle and used the iron sights for shooting. You wont find better irons on a military rifle they you'll find on a M1.