You can shoot the .45 in CDP, but if it's GI sights that might be more of a challenge for you than the trigger. You'd really want 3 8-rnd mags to start. I could be wrong but it looks to me like the Match 10 is legal for ESP division loaded to 10+1. I see nothing to disqualify it for ESP.
You should ensure your holster meets the criteria in the rulebook, but I believe it would be 'normal' at a local match to allow some exceptions so you can shoot a match. We almost let a guy shoot who came all holstered up with one of those tactical jack/Lara Croft thigh thingies, but I think MD said that's pushing it a bit.
Ammo that you know feeds well and is well matched to your recoil spring setup is about the only criteria for a local match--no one is going to check to see if you're 'cheating' with low-power loads, and I guarantee it won't make a hoot of a difference even if you were. In .45 ACP, I shoot 255 grain round-nose flat-point cast bullets with a light load of Clays; lots of folks prefer to just do your 230 gr FMJ or LRN with whatever pushes them at 750 fps or so.
As for 10mm, as I've never seen one, I know nothing about ammo. I'd go the lowest power commercial ball you can find, or you load up what you think just makes the 125,000 PF floor. Then, let me shoot about a 5,000 rounds through it, just to make sure it's "okay".