1911jerry, on Aug 24 2009, 09:45 AM, said:
1. Do you take your regular range bag? I have a Shooters Connection big bag, do I pack it in a siut case, use it as a carry on or what? Maybe just the inner bag?
Use the regular, full size Shooters Connection bag. Go with what you know and I check mine (pic added below)
2. Do you just buy a cooler out there and leave it out there?
Go to Wal-Mart, buy a styrofoam cooler and 1-2 cases of water and a bag of ice. Get back to the hotel, fill up the cooler with water and ice and leave it in the trunk of the car over night. By morning, replace with more ice. When the match is over, find a trash can for the cooler and donate the water to the club or the hotel cleaning crew.
3. Do you pack your holster, or discretly carry on in a paper sack, or back pack?
It's inside the same checked bag as my range bag (see pic added)
4. After I win HOA, what do I do with the trophy, pack it or carry on? JUST KIDDING FOLKS !!!!!
You have your clothing bag for any "trophies" or trinkits from the match. 
Usual load out for the match is that inside the SC bag will be my pistol and if they're not looking closely 300 rounds of ammo, belts, tools, mags, etc.
Inside the "big" bag is the SC bag, spikes and anything else that I may need for the match. Good place to throw a towel (hint).
Here it is all closed up. Well under weight and size limits and has wheels and a pull handle. $40 at Target. I generally throw a nothing pad lock on the zipper tabs and then a brightly colored zip-tie as well. I emphasize the brightly colored ones as white and black are pretty common.
ZERO hassles or issues flying to matches for the last 12 years.
Rich
(Since it'll come up, if they "find" (I'm not hiding it, I'm just not declaring it) my ammo, I take it out of here and then throw it in with my clothes. No big whoop.)