Congrats on the Kimber, it's a top shelf 1911.
I've got a Kimber Pro CDP II 4". For general practice, the Remington UMC FMJ 230 grain works great. For defense, I use the 230 gr Winchester Jacketed hollow points from Walmart in my area. The only issue I have is that my mags are 8 rd and it's very dang tight to get the first JHP chambered. Once the first round is chambered, totally reliable firing.
hollow points are going to be tricky to find what works best in the gun and with the magazines.