You don't even have to build a closet trap. You can buy a simple target bag, or build one if you prefer, and just shoot that.
As far as strength goes, I would take the bow and draw without an arrow nocked, then hold for 10 seconds, as many repetitions as you can for 2 sets with each arm. You do this with each arm so you do away with any muscular disparities in your back and don't cause yourself problems. Work on your draw stroke and form at full draw. Explore what your strength levels are, and make good decisions about how much to do.
It's not super cool like flinging arrows and playing robin hood, but it's a sustainable approach to learning and adaptation. The more bad habits you learn in shooting form, the more you have to unlearn.
The first adaptation you have to any muscular exertion is neural. You're teaching your muscles how to use all of the available fibers they can use for that movement and resistance before you actually start growing more muscle. But you will also, over time, be adapting your connective tissue (tendons, ligaments) and bones like the shoulder joint and scapulae. You can dig up a longbowman and spot him by his shoulders and scapulae because archery produces enough stress to cause these bones to change relative to other weapon or tool usage.
So, it's not just a matter of "working up to it" because establishing the kind of strength you need to shoot a recurve or other trad bow well takes time and discipline, regular practice, and attention to detail of shooting form and draw stroke.
There are a lot of people who will say "ah, it's not a big deal. just start flinging arrows." but those people can't usually shoot a bow accurately and have -0 knowledge about physiology and conditioning.
Trad bows are not for impatient people, though a lot of impatient people buy them and they wind up in closets or garages gathering dust. Exercise patience and institute regular practice that focuses on form. Your body will adapt and you'll actually be able to have better accuracy than a pie plate at 10 yards like most people who have a trad bow and don't do these things.
