You will probably end up with all of the above, mostly depends on the type and size of hole you want to drill or reamer size. When you factor in that you may use a center drill and then switch that out to various size drills, a 5/8" keyless chuck would be the most commonly used. There are many variants, the one I use I have never had an issue with it getting too tight. Drilling holes over 1/2", I either will use S&D drills if I need something quick and not too deep, but more often I use MT3 drills. I find that they have a sweet spot speed wise in different materials, so nice to have variable speed to dial it in. I also have a few MT3 stepped drills where the tip follows a guide hole followed by a shoulder drilling a larger diameter.
As far as a collet system in the tailstock, ER32 or ER40 collet chuck are the most common that I have seen. I use them to hold endmills when I want to square up a shoulder in a hole. Otherwise way too cumbersome to use. You also need to be careful of pullout from the MT3 as there is no drawbar system. An ER system is more accurate then a drill chuck and holds more securely, but you are limited more by the accuracy of what you are holding.
In addition to the above I have a dedicated MT3 tap and die system which can either be used manual or with power, I use it very frequently. Drilling large holes that you do not want to bore, there are MT3 annular cutter holders that are real time saver alternative to boring in stock under 2" thick.