Push drill is good for some holes but nothing below 3/32” or so for me because I tend to snap them.
I have MF #2 and #5. The #5 is a much better size for smaller drills. The #2 is a little too large IMO. A #4 would probably be the best for really detailed work but they are harder to find and the price tag usually matches.
The Buck Rogers drills, 104 and 308, are a good option too. They are more compact so you can get good control with more capacity. I don’t recall what the low end of the chuck is, it might go to zero on the 104 which has a 1/4” max capacity.
I can get some pics and better measurements when I get back home this weekend. Unsurprisingly though, I’m firmly in the Millers Falls camp 😉 I have to admit though, I don’t use eggbeaters a lot. A cordless drill is my preference and when I drill small pilot holes for small screws, I tend to use a push drill. Like I said, under 3/32 or so is about the only time I use any of my half dozen eggbeaters.