What is the tiny-hand most-friendly sets to migrate from duplo to lego?
As a conservative approach I would suggest the LEGO Juniors series which has cars and other sets and that are easy to build. 

However, from first hand experience I can tell that kids learn quickly. Even if reading instructions is too difficult, playing with regular LEGO parts will soon be a lot of fun.

Besides : Losing small parts will be an issue with each and every LEGO set. Maybe you could consider buying used sets or even used bulk LEGO. 

EDIT: LEGO Juniors is now called 4+, but it is the same product line.