I haven't tested it but I thought you needed at least two caverns to get underground trees.....
One cavern layer gets you ample underground trees. From the 3-layer behavior, I'd expected to not get bloodthorn or nethercaps; in practice, I usually get bloodthorn, but not nethercap.
I tend to go with the settings ral mentioned, higher min openness and low max passage density, since I prefer large, open spaces for my caverns. I also usually bump up the min water slightly, since I want to guarantee at least some cavern water. The world gen parameters let you set the 'depth' of your single cavern as you wish - if you just set the number of cavern layers to 1, you simply 'lose' the space taken up by the 2nd and 3rd caverns and the solid areas in between. By upping the parameters for z-Layers above First Cavern and z-Layers above Magma Sea (I forget what the options are named, but they're there), you can manually set the depth as you wish.
I used to add some z-layers above the first cavern, to given myself more room to build the bulk of the fort, and to preserve more z-levels for creating my trapped entrance hallway (needing several z-levels to accomidate magma reservoirs / pumping / spreaders and such), which was a remnant of my 40d designs.
More recently, I've moved to building my fort primarily in the z-levels of the cavern, and between it and the magma sea. This leads to rather cramped confines, since sometimes there are (by default) no full z-layers between the bottom of the caverns and top of the magma sea. Since my forts tend to be small (30-ish dwarves, and their bajillion children), this can still work out, but for a 200 dwarf fort, it'd probably be good to add a couple of z-levels in there. The 'benefit' (aside from fun & preference) is that I no longer need those extra z-levels near the surface, since all of the default z-levels (technically 5 z-levels, but usually more in practice) are available for use creating defenses, if I want to enable surface access at all. That lowers my total z-level count, which in theory should help with performance.
I don't tend to see the 'free magma pipe in bottom-most cavern level' you mention, however - that's only been in one of my DF2010 forts, out of maybe 20 or so I've done with a single cavern layer.