What make a good/secure exterior door?

The door is only as strong against forced entry as the Jamb. Reinforce the jamb with a steel strike plate that has at least 4" long screws that go into the wall stud. If the doors don't shut properly the hinges need to be tightened and adjusted. The doors could be warped and you will have to replace them if they're too bad.

A metal door is definitely best, but keep in mind that the door itself is NOT the weak point that is exploited when someone breaks in. It is the striker plates and locks that are the weak point. Make sure that you use large and sturdy striker plates with long screws and good quality lock hardware. Also you may want to take a look at the frame where the striker plates mount, if its not well build and well reinforced its possible to break the wood right out with the striker plate and lock cutout still intact.

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There are (expensive) commercial door and frame assemblies that can provide a high level of entry resistance.
These are rarely found in residential applications. Even when metal doors are used, they're usually mounted on standard wooden frames. These are often broken away when forced or can be flexed when pried to gain entry.
Saying all of this, a good exterior door is a metal door that fits snugly in the frame. The strike plate should be reinforced and connected with long screws into the stud behind the frame. A high quality deadbolt with at least a 1" throw should also be fitted. This is the "standard" that is recognized as being sufficient for residences.
You may have to replace both door and frame if your frames are cracked and weak.
I will tell you that I had all of this and the door was forced hard enough to snap the deadbolt out of the lock assembly.

Hollow metal doors with security hinges work best for your problem. About $50 for the frames, and 200-500 for the doors, depending on what style you want. If a burler wants in bad enough, though he'll get in...If he's good. Yer best bet is to get a big mean dog for when yer away. And to have a nice shotgun by the bed, if yer prone to this sort of activity.

Buy a metal door. there great.