Let's see here. The case listed for the 22 Hornet in the following manuals...Lyman 48th edition - Winchester; Hodgdon's 2006 edition - Winchester; Nosler (newest) - Winchester; Hornady (newest) - Winchester; Sierra (newest) - Winchester; Speer (newest) - Winchester. I see a pattern. I am not saying that Remington is inferior, I am saying the load data for all these companies were developed using Winchester brass - so that is what I use when I can. As has been stated, the Hornet case is very thin no matter which brass you use, so high pressures will shorten case life considerably no matter which one you use.
As far as bullets, powder and primers are concerned - you will just have to see what works for your gun. Many have had good results with Lil'Gun, I have not. Some have had good luck with 35 and 40 grain v Max bullets, that has not been my experience. Many use small rifle primers, I prefer small pistol primers. If you try Lil 'gun, V Max bullets, small rifle primers and find it to shoot well - great, many have. If you find they do not do the trick for you, try 12.4 grains of H110, CCI 500 primer and a 34 grain Mid South bullet and Winchester brass, which is a starting load in the latest Speer manual using their 33 grain bullet. I have had good results using Hornady's 45 grain Hornet bullet also, but you will need to back off the H110 considerably. For me, the journey to load success is the fun part, it is so satisfying when I get it right.
Good Luck and Good Shooting