Congratulations!
I have a P01, P75 Compact, and PCR (bought in that order, the Compact and PCR about a week or two apart, the P01 and Compact about a year apart). I like the PCR best. Probably because I wanted one since it came out and only bought it about a year ago. I got the P01 when I did because it was time to finally get one of the compact CZs and the PCR wasn't in stock anywhere, and since I really wanted the PCR, I didn't warm to it (until I got the PCR- now I love all three). I like shooting the Compact the best, while the PCR and P01 are heavy enough to be comfortable at the range, the Compact is a few ounces heavier and that much easier to shoot (I could shoot it all day if I could afford the ammo). However, I carry the P01 the most. Probably because I've had it the longest, shot it the most, and thus I'm most used to it (not that there is much difference).
I think these are about perfect carry guns. Light and small enough to conceal easily in most/all casual and business casual clothing (suit and tie might be tougher). Heavy enough for quicker follow up shots, long enough sight radius for good practical accuracy, and the grip has room for your entire hand.
As for your considering new grips, I have the original plastic on the Compact, the original rubber on the PCR and VZ grips on the P01 (probably the biggest reason it is the most carried). VZ, or any G10, grips are thinner than the rubber on the P01, making it an even better carry gun.
You asked about holsters a few times. I like hybrid IWB holsters for larger guns like these. If you prefer all leather, I'd go with something with dual straps or clips to spread the weight. I have hybrids for other guns from Foxx and Theis that I like, and use a Black Arch hybrid for my CZs. Black Arch and Theis are my first choice.