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Any hard-sided case, including the one that your pistol came in.
I generally use the traingle-shaped cases because they are much more compact.
Any decent small padlock is fine. Be sure you have the key in your pocket, because some will want you to open the case.
Pack the ammo separately in the box you bought it in, or a commercial box that fits it. It need not be locked up.

When you present your luggage to be checked, tell them "I have a firearm to declare".
They will give you a small form to sign, and a tag to go inside your luggage.
They will instruct you to carry your bag to the adjacent luggage acceptance area.
Once there they will ask if it's locked, and may want to inspect it.
They do recommend you buy one of their official locks, but I've not done that.

Once in california, just pick up your bag as usual and head out.
For travel through CA, just leave it in the bag as-is until you get into the U.S.

This has been discussed here at great length (see archives).