The instructions for your lathe say the chuck has threaded studs that go through a flange on the headstock and there are nuts on the back of the flange holding it on. Does that look like the setup you have? You will probably need to adapt a mounting plate to fit your lathe to use a purchased chuck like the one I posted from Shars.
Another option is to completely build your own. You would need to be able to cut a very accurate taper and thread for the nut (assuming ER style collets). There are a few threads on the forum discussing it.
For the size range you asked for, ER40 is a good choice. And a chuck like the one I mentioned is open on the back so you can have any stock that will fit in the headstock bore.
Creativechipper, have a look at the above. It is accurate.
If you wish to use an ER collet chuck on your lathe then you need to first find a backplate with a spindle mount that matches your spindle. There is a taper on the back of this backplate that must match the taper on the nose of your spindle. It must also have the three studs needed to mount said backplate to the spindle. The front side of the backplate will be bare. You must machine it flat and drill and tap holes in it to mount the ER chuck.
DROPros sells a backplate for this lathe for $26.99. Once you have the backplate in your possession then you need to measure the diameter of the plate and find an ER chuck that you can mount on it. Many places sell ER chucks that have a flat back that allows you to mount it to a bare backplate. I won't go into details on how to do that here; you can start a thread for advice on how to do that.
Once you mount the chuck to the backplate, it is ready for use. You slap a collet into the chuck and do your thing - hold stock for turning, hold an end mill to mill something in a milling attachment on your cross slide or whatever. Since your spindle is slightly over 1" (you need to confirm this diameter before choosing a chuck), an ER-40 that uses collets up to 1" will be your best bet.
I hope this clarifies the process for you. None of this is hard and you can do it. You need to be able to face the backplate and then use a transfer punch to mark the location of the chuck mounting holes, then spot the holes and then drill and tap the holes before mounting the chuck. After that, you're good to go.
An ER chuck is useful for tool holding. It will hold work also but, in general, is appropriate only for parts that have already been turned or are threaded. This is because an ER chuck is pretty accurate and will hold an already turned part pretty concentric, whereas that same part will not run true in a 3 jaw chuck. A threaded work piece can be mounted in an ER chuck without damaging the threads so it is useful there. Otherwise, a simple 3 jaw chuck will suffice for most hobby work; it will allow you to turn a work piece the first time and have it turn out concentric with the spindle. This is called a first operation. Once that part is turned and removed from the chuck, any further machining on that part is called a second operation and requires an accurate holding device to get it concentric with the spindle. A collet chuck or a 4 jaw independent chuck is typically used for this. So, other than tool holding or working with a threaded or second operation work piece, you really don't need to use a collet chuck.
