Architrave is easy, and much less work than stripping the old.
A carpenter should be able to do them all in a day.
S/he will want to nail them up. This will sometimes split the wood and is difficult to remove. My own preference is small screws. I find it easier to prime and undercoat architrave before fixing, you can carry it into the garden, and will have to apply the final coat after fixing to hide the filler over the nails and screws.
If you have an older house, don't get a modern architrave, which is narrow and simple. You can still get wide, moulded architrave, typically around 75mm wide.
When the architrave is removed, you may see gaps or cracks in the plaster round the door linings ("frames"). If you like, you can inject expanding foam. I like to use the pink fire foam. Clean out dust, and moisten the gap before injecting. The foam will stick the lining to the wall and prevent future rattles and cracks, especially if you have a teenage daughter.
If the foam is hidden by the architrave you do not need to smooth, fill and paint it.
Or you can use decorators caulk which is not as good.