The LP10 comes in a VERY nice lockable case. add a duffle bag or back pack for your shooting glasses, ear plugs, pellets, targets (you won't need these at SCAA but you will at HKRA), in fact, Pilk sells a nice rolling back pack the case will fit into! http://www.pilkguns.com/ppack.htm
does your arms license allow you to keep the air pistol at home? if not, you probably don't want anything larger than the case it comes with to fit the door in the armory.
However if you will travel (come here!) you should not carry a gun in a home-made case as luggage. they make VERY good cases for air travel and the locked LP10 case wrapped in a suitcase of clothes is probably safe and legal.
US NRA bullseye pistol shooters use a very fancy box to hold 4 pistols and a scope and a bunch of .45 ammo, but international shooters do not and air gun shooters don't use a scope. international style shooters usually have a commercial airline-trying int'l and who is primarily int'l
I don't even think there is enuf room on an international bench for such a box as NRA shooters use.
US pistols shooters