I'd agree, cross levers. If you fit flat bars, then you've a bunch of attendant problems to solve as well as the expense of new levers and gear changers. I would only go down that route if the cross levers don't suit.
Funnily enough my wife has just gone the other way to a drop bar bike. She did choose one with hydraulic brakes as the feel and force were immediately more reassuring than cable discs or calipers. It was also easier to adjust lever reach. She was also trying to solve a carpal tunnel problem and the varied positions available for drop bars were an immediate benefit, something to bear in mind.
She did say the new bike feels twitchier that the mtn bike she's coming off, which it is bound to and there is always some adaptation to do. The other thing to consider is bar shape and width. It could be that changing the bars could also be beneficial, what you need to do is find a store and peruse some drop bar bikes to see what might suit