If this is a dual purpose gun, then make the CCW portion the priority. Don't buy anything you haven't shot and know you can shoot well -- your life might depend on it!
There are lots of good guns in the $400 range - although you might need to consider used depending on the brand/model you want. Have you thought about how you will carry -- IWB, OWB? How hard will it be to conceal a pistol with your frame size? Skinny, 5'2" guys have a hard time concealing a full size 1911. On the other hand, I've seen guys that could hide an M1 Garand in their pants and no one would know it! Your body type and holster choice may drive some of your options for your pistol.
Right now, my two carry weapons are a Walther P99 and a Beretta PX4. I would highly recommend you consider the PX4. It's right at the edge of your price range ($420-$450) but well worth the money. I wouldn't recommend paying the $500-$600 to get a Walther when you can have a PX4 for much less. The pistol conceals very comfortably (I'm 6 ft, 220 lbs with some "love handles"). I carry in a Comp-Tac Pro Undercover IWB holster and spend 2 1/2 hours a day in the car with no discomfort with either pistol. By comparison, carrying my Sig P228 in the same style holster was a constant pain in the back and I stopped after a couple of tries. The polymer frames on the Walther and Beretta make a big difference -- the Sig was just too heavy.
Another option would be a used Glock 19. Glocks are pretty reliable used guns -- they're almost indestructible. Again, you need to try one and see how it fits your hand and how you shoot it. No sense spending $400 on a pistol if you can't hit anything with it!
I have 3 CZ's, but not a PCR or P01 so I can't comment on them. I can tell you that the P01 didn't fit my hand as well as the full size. (That's not a problem for me with the PX4 -- the interchangeable backstraps make it easier to customize the gun to your hand.)
Any of the above pistols would be competitive in IDPA - but I still recommend that you get the gun to meet your carry needs first. Odds are that whatever you end up with will work just fine for competition, too.
Good luck!
Jim