Hi @Skyegirl21 ! May the Force be with you as you work through your project!
I think the "best" way would be to remove everything. However, having inquired with two professional painters I have worked with, they look at me like I have two heads when I ask if they will take the door down and remove the hardware.
I suspect the paint levels better horizontally (duh!) but the way I've come to look at it, depending on usage and location, the darned thing may have to be repainted some time in the future, anyway, so to attain that "perfect" finish today may not be worth all the effort given that they all see scuffs, marks, fade and chips over time.
I like the idea of painting your hardware! I've done that with house numbers, to match the door.
The painter I'm working with will be here soon to re-paint my front door. He's just got to knock down some sheen and work out some (bad) texture issues. I'm using semi gloss on the door but we used the soft sheen on the shutters and it's nice. My door is under a large porch and in a corner so some shine really helps it sit proud of the darkness. Just not high gloss. What a disaster.
Let us know how it goes! Remember the principles of wabi-sabi (acceptance of transience and imperfection; appreciating beauty that is imperfect, impermanent, and incomplete). Helps me, anyway!
Cogito ergo sum