I haven't even been in my kayak this season because I am having a great time on my boards. My advice is to take a lesson and/or join a club. We started a SUP program with Colorado Whitewater, but it isn't a good idea to jump on whitewater without some instruction.
Gear is important, so all of the advice given so far is great. I would wait until the water comes down a little and I don't even recommend a leash for first time SUPers on the river. If you have a strong group and you have selected a good stretch of river, then losing your board should not be an issue.
I will send you a PM and feel free to e-mail me with any questions. I LOVE to recruit new SUPers.
It is fantastic and you might decide you like it better than kayaking. To me it was like giving up the skis for a snowboard. Just less stuff to deal with.