(May want to repost this in "Central Region" for more viewers. Just a suggestion.)
Dozens and dozens of trips on/around the BNR. Been here my whole life...
Late March will be just fine. Based on spring rains, you may need to keep your put-in flexible. If things are really up, you may be able to start as far west as Ponca or even Boxley. If not, you'll need to check into Steel Creek or Kyle's Landing. Regardless, I would suggest starting as far upstream as possible for two reason: 1) The Ponca Wilderness area is spectacular. Take your time here, and do
plenty of side hikes exploring the many bluffs, waterfalls, and pre-National Park homesteads, schools, and churches/cemeteries; and, 2) unless the water is very high, the lower river (downstream of Hwy 65 bridge) will be slack and require much more paddling, which gets very old and tiring after 5 straight days.
The other option, if you're interested is staying in the boat, is to cover the whole river. I did a 171-mile float from the Upper Buffalo Wilderness (up where the river is still referred to as "creek") to the mouth at the White River near Buffalo City in five nights. But you gotta be movin' fast, and you'll likely portage much of the upper reaches. Ouch.
No matter what you choose, you'll love it, I'm sure. The place is amazing. Every gravel bar is open for camping, and that time of year you'll have no problem finding some solitude. You may even go some days without seeing another person. Yeah, it's that good.
Best of luck, and make sure to post up the trip log and pics when you get back!