Any of the 240gr. to 300gr. 45 caliber bullets can be used on deer in the Casull. However due to the power (velocity) available with the Casull, you must choose a bullet compatible with the intended load for good hunting performance.
The bullet makers generally provide loading data suitable for hunting with their bullets in the Casull. About half of the 300gr. bullets can be used in full power Casull loads. But those high power 300gr. loads are more than needed for deer. Bullets in the 240gr. to 260gr. range were designed for 45 Colt loads (both standard pressure and the higher Ruger/TC/Dan Wesson pressure loads) and are also suitable for deer if their velocity is limited to levels below full power. The Hornady 240gr. XTP-MAG is an exception and is designed to work at full power Casull levels.
The tough 300gr. and 240gr. XTP-MAG bullets are really intended for game tougher than deer. They can be used on deer, but they may not expand much. Of course, when you start out at 45 caliber, expansion is not as important. Unless you really enjoy and prefer to shoot the full power loads, I would suggest something a little lighter.
Good deer loads can be assembled with the standard 240gr. to 260gr. bullets from Hornady, Sierra, and Speer. As suggested above, HS-6 makes an excellent medium power powder for the Casull. I've used 15.5gr behind Sierra's 240gr. JHC and it makes a very manageable load that could be used for deer.
True Blue is another powder that can be used to assemble nice manageable loads for the Casull. Sierra's 240gr. JHC ahead of 14.0gr makes another load suitable for deer hunting that's fun to shoot. Both this and the HS-6 load above can also be increased some if desired. Check the data available from Hodgdon's and Western Powders' websites for further details.
If those loads aren't exciting enough, 2400 can be used for more recoil and muzzle blast. You can start out at about 24gr. and work up from there with the 240gr. to 260gr. bullets.
The Casull uses small rifle primers and I see the CCI SR, WSR, Federal 205, and Remington 7 1/2 suggested most often. The Remington 6 1/2 should not be used. It is designed for lower pressure cartridges.