I use the following on my Shopsmith
5/8" to 1" x8 TPI adapter from PSI
Barracuda 2 scroll chuck from PSI with. I use this for bowls, spindles, and drilling pen blanks.
Collett chuck from PSI also used for detailed turning, drilling round stock, threading
1/2" MT2 drill chuck from HF for holding the drill bits/taps when drilling or tapping on the lathe.
A word of advise on drilling with the lathe on the SS. The tailstock likes to flex against the pressure of the quill. just don't push so hard and let the drill do the work. Clear the hole often. Make sure that the drill bit is alligned correctly with the headstock.
Remove anything attached tot he quill.
Install the drill chuck in the eccentric of the tail stock.
Insert your drill bit and hand tighten
tighten with the chuck key using all three points on the drill chuck
move the headstock to the drill bit and check the alignment. There is a dimple in the end of the quill the point from the drill bit should line up dead center with that dimple. You may have to adjust your eccentric and/or the height of the tailstock adapter to get the alignment where it's needed.
Always start drilling with a starter bit or dimple the center of the stock with a skew, this will keep the drill it from skating on the surface of the material.
Terry