I'm 5'9" and I generally use 42cm bars. I have a set of 40s I will probably try on a bike soon, and I'll see how those feel. On a touring bike I'd probably want the wider 42-44cm bars. Just a guess.

IMO bar end shifters are your best bet. Unfortunately, you will likely not be able to mount any sort of MTB shifters on drop bars unless you get a really crappy set of old steel drops that have the smaller MTB diameter. Almost all decent road shifters are expensive (compared to MTB trigger shifters) and I haven't figured out why.

Another possible option is to take some old clamp-on MTB thumb shifters and fit them somewhere on the drop bars. The older cheaper ones often had flexible clamps that you can make work on drop bars. I wouldn't recommend it, but it can work.