Get some good glass!
I'm a Nikon man myself so can only really speak for them. For a special day like that you might want to consider hiring a really good lens or two. Something like a (stunningly good) Nikon AF-S Nikkor 70-200mm f2.8G ED VR II brand new will set you back about £1500 at least. The same lens will cost about £50 a day to hire if you shop around.
Calumet (assuming you're in the UK) do a very impressive wedding lens hire-package including a very decent flash for £120 - http://calumetrental.co.uk/wedding-lens-package-nikon.
For the indoor shots and reception get something like the the Nikon AF-S 35mm f1.8 G DX Lens. Superb lens and should set you back no more than £100 quid if you shop about, and very fast for those darker shots. Plus not using the flash will get some really good photos highlighting the DJ's lighting during all the dances at the end...
PParker142. The Canon 5D III is a really good Camera. I'd be tempted to stick with that to be honest. D3200 is a good camera for beginners, but nowhere near as good as yours I would say. If you're really looking to update look more towards the Nikon D7100 or the Canon 70d or 7d (Not quite sure what the US equivalent would be...) for the equivalent of what you have now.