Hanging blinds from a metal door

I'm changing the broken blinds on the inside of my exterior house door. I was hoping the new ones I bought at Home Depot would use the same brackets as the old one, but they don't. So I took down the brackets that the old blinds used and am starting from scratch. The door appears to be a hollow metal door. I've attached a photo of what the old holes look like, as you can see from that it's a metal door.

My question is, what do I need to get the job done? After a Google search it appears I need to drill some new pilots holes with a carbide drill bit after measuring the new blinds against the door and getting the placement correct. The consensus seems to say to use a center-punch to create some divots for the drill bit before drilling so the bit won't slide on the door. After I drill my pilot holes then I can use self-tapping metal screws to fasten the brackets to the door itself.

This is the early plan. Should I go with this or is there anything I can do differently that might work better? Also, how much smaller should my drill bit be for creating pilot holes versus the self-tapping screws I'll be using to fasten the brackets to the door? Thanks in advance.

 

You don't need any special drill like carbide. Any twist drill intended for steel will work. You can center punch your hole location or just go at it with the drill. You'll likely need a small size drill and they start relatively easy.