If you get a standard carbine RE, make sure it's milspec and made from 7075. I know the milspec carbine RE made by MagPul is 7075. If you get one from PSA, be very careful. Some of their "milspec" REs are made of 6061 and they aren't always clear about which one is which. With a carbine RE, you use a carbine buffer and a carbine spring.
Verify what buffer and spring your current RE uses. If it uses a carbine length buffer and carbine length spring, it will fit in a carbine RE. However, if the buffer is longer, such as a rifle buffer, you'll also need to get a carbine buffer and a carbine spring to go with the carbine RE.
I would recommend an A5 style RE assembly over the carbine RE. It helps your AR shoot a little smoother. You don't need an A5 style RE assembly, but if you're going to spend the money on a new RE anyway, it's worth taking a look at.
The two most popular makers of the A5 style RE is VLTOR and MagPul. The VLTOR is called the A5, the Magpul version is called the SR25/M110 Enhanced RE. Both use the A5 length buffer and rifle length spring. Which to get is up to you. VLTOR makes a 6 position and a 7 position RE. The Magpul has 10 positions. I used the 6 position stock with the Carbine Fixed Length. The "ridge" is shorter which allowed me to make a spacer that was a bit longer for more LOP. For an AR I will use and adjustable stock, I will be using the MagPul RE with its ten positions.