>>1936471You need short pull brake levers.
This is defined as the distance between the pivot point and the cable anchor.
It is a continuum, not a binary. Less than 30mm is short pull. More is long pull.
V-brakes and mechanical disc brakes are long pull, so most newer brake levers are not compatible.
Cantilever brakes are short pull, so many older flat bar brake levers will work well. Old Deore XT is basically the nicest you can get.
Some like pic rel, or old LX, have adjustable pull ratios.
Also if you find an integrated brake/shifter, and you just want the brake part, it is quite easy to cut it off with a hacksaw and file. Many of the brake levers I run are like that, as integrated units with broken shifters are thrown/given away.
As for what style of bar you want, you should determine that based on fit. A pair of ~600mm bars with 40-60mm rise, and maybe a little sweep, is probably the best thing though. I don't really advise a moustache bar. Nor any swept cruiser bar. Just going from drops to risers will give you significantly less reach already.
You should also consider integrating a front basket into your plans, especially if you get a meme bar with the controls back from the middle section (those cable easier with them).
I also want to see your current setup and advise you to consider keeping drop bars and getting a taller/shorter stem.