What kind of screws for attaching an Ikea style coat hook of an internal door?
If your door is hollow (easiest way to find out is to knock on it) then you will need to use toggle bolts.



The downside to these is that you need to make a relatively large hole to get the bolt through.  You might be able to get away with smaller or different anchors, but you specifically mentioned that you wanted to hang heavy objects, and these are best for heavy loads.  Make sure that the screw is not too long otherwise you'll never get it tight enough as it will hit the other side of the door.

If the door is solid then you can just attach it with wood screws (#6 or #8, 1/2 or 3/4" will do the trick).  You should pre-drill a small hole prior to prevent any splitting/cracking in the wood.

In both cases you will end up with holes in your door which is often undesirable.  They also make hooks specifically for doors that hang from the top of the door instead of requiring anchoring into the door itself.

The other thing I'd mention is that inside doors aren't usually designed to hold loads like this. You might find that overtime the door will shift.  You can probably mitigate this by driving 3" screws through the hinges on the wall side so that they are held up by the stud and not just the door frame.