All depends - melamine coated board will not need finishing so as you want it to be a quick job, that might be best. Just be careful about cutting it without chipping the melamine - I use a router, but there have been some recent threads about this. Wood veneered board would, in my view, be nicer to work with and wouldn't need too much finishing. Plain MDF would probably need to be painted, so would take the longest.
MDF is probably better than chipboard as a core material, although most flat pack stuff you buy tends to be chipboard. I've not used ply for this sort of thing.
Whatever you use, I would always go for 18mm rather than 15mm board
Just one other point on design - I think wardrobes are often very wasteful of space. Most have a shelf at the top and one hanging rail under that. If you only want it for jacket-length clothes, I think a better arrangement is to do away with the shelf at the top and have one hanging rail at the top and another half way down. That way it holds twice as many clothes. Depending on the size of the wardrobe you might want to insert a shelf half way down, using those same knock-down fittings, purely for stability.
Hope this helps.
Paul
PS I know people knock IKEA, but have a look at their stuff for ideas - I think some of their designs are brilliant. And if anyone knows about knock-down furniture they do. Go in the evening during the week - it's not usually crowded then. I'll now run for cover 8-[ 8-[
