Good man Jeeper
You have chosen a great sport IMO. It is also one of the most challenging, and one that every rifleman could profit from.
My opinion is that you should use a very accurate rifle/ammo combination from the start. My feeling is that the CZ is a great rifle for the price and should acquit you well. The problem with a rifle that throws a 3 inch group is that you will find yourself chasing misses. If you shoot dead on and miss, you will try to correct for the miss and then miss even further. You want the misses to be your fault not the equipment. That way, if you miss, you know that your hold was less than perfect and simply strive to hold better, not chase misses fruitlessly.
Shooting as well as you can will bring you back for more, and doing poorly because of equipment will surely discourage you. The guys that you are going to compete with are usually veterans of the sport, and you will require time to get your feet under you in the sport, so don't get discouraged, and give yourself time to shoot to your potential.
I LOVE shooting silhouette of any kind. You get the instant feedback of a shot well done, and the pain of a miss instantly also. It has the all the thrill of hunting IMO, except that you get the thrills for 80 rounds if you shoot both hunting rifle and target rifle. One of the most rewarding days of shooting I can imagine.