You can always use a threaded to threadless adapter, but I think they are almost always ugly, and won't eliminate the flaws of quill stems. But it will give you a wider choice of stems and bars. Otherwise, yes, you'll need a new headset, forks, and stem. Also depending on your choice of stem you'll possibly also need a new bar (newer stems are generally only made for oversized bars), and a shim to for the stem.
Threaded headsets did come in various sizes, but most likely your bike has a 1" one (check beforehand). Your choice of forks will be somewhat limited since most new forks are in 1.125". Best to look for NOS steel forks with uncut steerers. Then there's the problem of the headset, since most threadless ones are in 1.125" as well, so you'll have to look around a bit. SJS still has threadless 1" headsets, and you can sometimes find very nice NOS 1" Campag ones at various places (e.g. Hilary Stone), but again, they are not common. If you choice of headset does not come with an expander/star nut, you'll also need to find one of those in 1", again SJS has them. Also you'll need a stem shim to fit newer stems made for 1.125" steerers on to a 1" one. Consider it's just a beater, it might not be worth to go to all this trouble.
You may also luck out and discover that your bike has a 1.125" threaded fork, then ignore everything above since finding 1.125" threadless parts is pretty straightforward.
You can always use a threaded to threadless adapter, but I think they are almost always ugly, and won't eliminate the flaws of quill stems. But it will give you a wider choice of stems and bars. Otherwise, yes, you'll need a new headset, forks, and stem. Also depending on your choice of stem you'll possibly also need a new bar (newer stems are generally only made for oversized bars), and a shim to for the stem.
Threaded headsets did come in various sizes, but most likely your bike has a 1" one (check beforehand). Your choice of forks will be somewhat limited since most new forks are in 1.125". Best to look for NOS steel forks with uncut steerers. Then there's the problem of the headset, since most threadless ones are in 1.125" as well, so you'll have to look around a bit. SJS still has threadless 1" headsets, and you can sometimes find very nice NOS 1" Campag ones at various places (e.g. Hilary Stone), but again, they are not common. If you choice of headset does not come with an expander/star nut, you'll also need to find one of those in 1", again SJS has them. Also you'll need a stem shim to fit newer stems made for 1.125" steerers on to a 1" one. Consider it's just a beater, it might not be worth to go to all this trouble.
You may also luck out and discover that your bike has a 1.125" threaded fork, then ignore everything above since finding 1.125" threadless parts is pretty straightforward.