For the tailstock just get a good Jacobs drill chuck.
I use a 3/8 inch keyless for small bits and a 1/2 inch chuck for the bigger drill bits.
Wholesale tool has a big selection, pick out the chucks and get the MT3 arbors with the same taper to match. JT33, 2JT etc.
Plenty of cheap chinese chucks but the Jacobs are worth the money.