you can use an outdoor paint indoors
except that white oil-based paint tends to yellow if it is not in good light (close to a window will do) so a white water-based paint will stay bright better inside. (all the new low-VOC paint formulae suffer from yellowing). The Dulux Trade Gloss in cans with blue lids is a revised formula that is supposed to resist yellowing indoors.
I have been quite disappointed with eggshell indoors, to me it looks like undercoat. I prefer Satinwood.
But oil-based gloss is toughest outside.
A power sander will be useful on flat surfaces, and a small detail sander for fiddly bits. Measure the width of the panels in your doors, as a large sander may be too big to fit. For mouldings and rounded surfaces do it by hand, your fingers will soon get stronger. Wear a mask and goggles, and get some blue disposable gloves. Scrape old paint out of the joints of a panelled door, filling them with paint will make the paint crack more.
As for the chips in paint caused by keys, look out for nice covered keyhole escutcheons, and finger-plates to match that you can position under the keyhole. Fancy brass edges are very difficult to polish, smooth ones will be easy. Stainless lasts longer than chrome. Drill the screwholes before painting, but take off all door furniture. If you are having new locks or hinges, or having the door planed to fit, get that done before painting. The furry "brush pile" draught excluder is good, verify that it will fit before painting. If you have several doors and are buying new locks, go to a proper locksmith and ask for them to be suited to the same key.
Pay special attention to painting the top and bottom of the doors, these are the most neglected surfaces, and the most likely to get water penetration.
If you are ever having the door hinges changed, I recommend you get lift-off hinges as they make it so easy to remove the door for redecorating or moving furniture.