Since you're going with flat bars you'll be getting MTB levers. V brake levers will not have the right leverage to work with dual pivot brakes. Using them will require a far more firm pull to stop at the same rate you are used to stopping. What you really want is the old school MTB cantilever brake levers. However a suitable substitute if you can't find the old spec levers is the Avid Speedial levers with the cable shuttle screwed all the way in towards the pivot as you can. Those still won't be quite the same but it'll be really close. True canti levers are only going to be found as used item. Avid Speedials are quite common with many online shops or through ebay.

I'll also echo that if this will be more of a sit up bike for a more casual sort of riding then you should get a frame that supports that. I'd look at Cyclocross frames and 29'er mountain bike frames. Both will have the canti studs so you can use the V brakes and more modern levers. And don't worry about the 29'er being what looks like a dirt bike. They do take 700c wheels. Although your wheels are likely 130 mm so you may need to have some spacers added to get them out to 135. There's no reason you can't use them if that is done although it's not common.