Sue, if you can possibly return the lathe you have to H.F. and buy the next size up (picture posted by Charlie) it would only cost you $75 extra and would be well worth it in the long run and would save you buying the drill press.
What will it gain you ? -
- longer length to accommodate your headstock chuck, jaws, pen blank, drill bit and Jacobs chuck (in the tailstock)
- more common MT2 (instead of MT1) fittings in both headstock and tailstock resulting in easier-to-get accessories
- MT2 gives you better accuracy and ease of use (as well as easier-to-get accessories)
If you are at all serious about this hobby you will come to appreciate MT2 and the extra lathe length.
Whatever lathe you have ....
Before you buy a headstock chuck, you need to find out the thread size on the spindle in your headstock. The lathe you have shows (in the picture) a faceplate attached to the headstock spindle. If you remove that faceplate, by unscrewing it, you will see the threaded end of the spindle. Quite likely, the thread size will by 3/4x16. That means the outside diameter of the threaded part is 3/4" and the thread spacing is 1/16" (or 16 threads per inch, which we call 16 TPI). You have to buy a headstock chuck with matching threads that screws on to the spindle. You may need to get an adapter, depending on the headstock chuck that you choose. A more common thread size for the spindle and headstock chuck is 1x8 (meaning 1" outside diameter of the threads and threads spaced 1/8" apart - commonly called 8 TPI ).
I hope these comments are helpful to you.