How to tell if your locks are bump proof

I think you answered your own question... "I don't especially care about being able to rekey the lock myself". If you don't want this feature, don't pay for it. Pick up a good sturdy lock from a trusted manufacturer, that has the features you want.

If you want to use the same key for all the doors in your house, you may be better off buying new locks for all the doors. Most hardware stores carry sets of locks; where you'll get 2 knobs and 2 dead bolts that all use the same key, so you can set up 2 doors to use the same key. You may be able to get sets for more than 2 doors, but they might prove more difficult to find.

Your key requirements should realistically depend on what your home insurer requires. If they specify a particular type of lock in order to meet a requirement / get a lower premium etc, then that is the type of lock you should fit.

Often apartments or managed properties will have a minimum requirement or a preferred supplier.

All locks do is delay a thief - certain types of locks will delay a thief more than others, but if someone wants to get into your property they will be unlikely to worry about the lock unless it is a very weak one. They will simply kick in the door or break a window.

Of much greater importance, if you are worried about break-ins, is to fit a door which has a strong wood or metal core, with multiple anchor points around the frame activated by a deadbolt lock, and ensure the frame is solidly affixed to the structure of your property.

(As an aside, this is why lockpicks are now legal in the UK and various other countries - only lockpicking enthusiasts, locksmiths, law enforcement and spies use them. Burglars use a brick, crowbar or their foot)