RFID protective case metal selection
The first place to look would be the frequency of the RFID system that the system would block. If there is one frequency this may make things easier, if the blocking needs to happen for several cards this might make design more difficult.

Here is a list of some of the systems and their frequencies:


Source: http://www.rfid-101.com/rfid-frequencies.htm

Now you want to build a faraday cage around the card to block any frequency from entering that area, a faraday cage works by conducting an electric field through the cage leaving the field in the middle at zero. Another thing to not is magnetic fields cannot be blocked, only attenuated, so if the RFID system only uses an inductive field, its best to stick with a magnetic attenuator like mu-metal. The field also can be attenuated by a material with a parameter called beta.

\$\Large{\delta = \frac{1}{\beta} = \sqrt{\frac{2}{\omega \mu \sigma}}}\$

Mu and sigma are values that are material parameters and can be looked up for most materials. With a higher skin depth you have less attenuation, so you want a material with a low skin depth that won't conduct far into the material a the RFID frequency you want to block. Here is an example of some materials and their skin depth:


Source: https://commons.wikimedia.org/wiki/File:Skin_depth_by_Zureks.png

Here is an example:
If we had a card with an RFID signal of 433Mhz that needed to be blocked (attenuated) with an 410 steel as a material, the signal would only travel ~0.02mm so that would be the minimum amount of material to block the signal.

A low frequency signal of 125kHz would need more material or ~0.05mm.

Its important to note that a faraday cage with an opening is no longer a faraday cage, this makes it harder to analyze and would take a few pages a lot of EM theory to describe, so try and approximate a cage as close as possible with your design. My gut feeling is this won't matter much if you keep the opening small or extend and make the sleeve longer than the card.

Testing should be pretty simple if you got a card and a reader, build a sleeve out of the material and see if it can read it.