There seems to be enough posts on here about safes and burglary. Every one has an opinion. Some from experience and some based on whispers and rumours. I would ask the basic question, why is access to the house so easy? It has been pointed out that family in the house (who one would assume are the houses most valuable contents) are vulnerable so surely that is the first issue before securing trinkets.
Having sorted that out, a safe needs to be large enough to hold the range of valuables that need to be secured. Bedside table size is probably the minimum if not bigger.
Crims need some indication that you are worth robbing and that valuables are on-site rather than in a bank or such. It also seems that the safe installers are prime suspects when the hidden location is so readily known. In general, most burglaries are either opportunistic or hoping for car keys etc. There are not so many of us that have assets so vast that a military style operation is worth the while.
My solutions;
Make your house far more secure. The first line of defence.
Get a large professional safe with fire and flood rating, there is every chance that one of those events will be the cause of the loss of your valuables inc papers etc.
Install the safe yourself if you have the skills, failing that use a very good security company rather than the cheapest you can find. The less people who know, the better. For most of us, there is no need to insure those contents as it then lists a safe on the insurance documents. In general, you are less likely to lose out than through fighting insurance companies.
Be extremely ingenious about location.
When all else fails, the dummy baby safe and some out of date credit cards etc, bit of cash may deflect the search if it was an opportunistic visit.