I may not be the best expert on the matter, but from what I read on these forums when I was just starting out with my bullwhip, I think perhaps the best case scenario in storing your whip would be storing them as straight as possible across some flat surface, or vertically hanging from the wrist loop (though this may possibly damage the wrist loop over time). This has to be done though out of direct sunlight, but in a reasonably well lit and airy area.
You don't want it in a damp place (obviously due to the moisture- mold, mildew, etc), and you don't want it in the dark either.
I'm in the same boat as you are- when I picked up my whips, I mainly wanted them for display purposes (which is why I'm upgrading to a display case!). The way I treated my own whips from the time I got them back around June '08 till the present seems to be working out really well, and what I did was to go out to a hobby store to buy a couple of wooden coat hanger racks (as I read that metal may react with the leather). I compromised on coiled them loosely, as coiling them too tightly would be bad in the long run, but I still wanted a coil for that 'look'. But remember NOT to coil it the opposite way though!
My display looks like this at the present, at least until I 'upgrade'! Pardon the mess...
http://i160.photobucket.com/albums/t167 ... MG3255.jpg
I probably should mention that as I'm using a thin 'peg' coat rack, it has a tendency to cause little kinks in the whip, so that when I uncoil it, instead of being completely straight, it has little V's breaking the line. However, I'm told that this is nothing to worry about, but IMO it just isn't as aesthetically pleasing. I suppose this *might* be avoided by using a thicker set of pegs? My coat rack looks very similar to something to this:
As for treating it? I don't think you really need to do anything special to it on receipt, and this is coming from someone that pampers the heck out of all his gear! I don't think Pecards is a good idea, as it should already be well treated on arrival, and adding Pecards (or any other leather conditioner) would only loosen the braids. All it needs are a very, very light dose of Pecards maybe every half a year depending on usage, but the main regular maintainence you should do is to wipe down the whip (from handle downwards) after every use so that it gets rid of the dirt that might get trapped between the braids, which could cause problems down the line.
If you're wondering about the backup falls as I did, I found the best storage solution would be to keep them completely greased up in a nasty over-serving of Pecards, stored in an air-tight container. This keeps them from drying out, as they are supposed to be backups after all, and would be useless if it snapped in half from being dry and brittle on their first use. However, it looks like some people on this board have kept theirs in the open without ill effects, so I guess this really comes down to how careful you are, as well as personal preference.
Finally, I don't know if this will help, but here's a thread I started when I first picked up my whips, which helped me learn a ton as far as displaying/storage were concerned:
viewtopic.php?f=3&t=26940
Hope this helps, and by the way, whose whip did you pick up?