I used to open safes and vaults for a large US bank and have a fair bit of professional experience breaking into safes/vaults (legally).
I would avoid safe deposit boxes many banks keep poor records and I have seen way to many safe deposit boxes that were drilled and opened accidentally (wrong box number written on entry card happened fairly often).
Things to look for in a safe for gold and silver.
The other consideration I would have is that it is important that you hide the location of the safe as best as possible.If a thief can't find it they can't steal it. Also if you are planning on storing documents or other things that could burn it would be a good idea to get a fire rated safe.
I don't think there is anything that will 100% protect your stuff from getting stolen but with a decent safe and some reasonable precautions you can thwart all but the most ambitious and skilled criminals.