The Goodell Pratt/Millers Falls + push drill screw chuck is, IMO, the best there was. It locks up very tight, no play at all once the bit is chucked. The early Yankee style chuck was not bad either as it too was a screw chuck, but then Yankee switched to a spring action chuck (similar to how all the electric drill/driver chucks work today). These chucks allow for a quick bit change, but the drills that I have seen with a lot of finish wear also were very sloppy in the chuck.
I realize these are not precision drilling tools, but my favorite push drill is an early (1915 patent date) Goodell Pratt 185. It has obviously seen plenty of use, but still locks up nice with no play. Eventually the Yankee style bit became the standard, and Millers Falls began offering their drills with the Yankee-style bits and they added an 'A' to the model name to distinguish them from the older models (wasn't the case with the 188A)
You can still find bits on eBay, although they can be pricy. Here is a seller (
link) that has multiple sizes for sale. Might be worthwhile to contact him to see if you can get a discount for buying more than one, as his price does include shipping. One cheap way to find these bits is to look on eBay for the Craftsman drills made by Millers Falls. The can sell pretty cheap and often are complete with a full set of bits.
Any particular size bit(s) you are looking for, or do you need the full set?