I agree with the other comments that this sounds much more like a worn out small cog. If the original owner tended to just leave the chain always on the small (14 tooth) cog, then this can wear out rather quickly. I've had bikes using a short-cage derailleur where the chain would hang completely slack in some ring/cog combinations and this still didn't cause any problem with skipping. OTOH, putting a new chain on a worn cog will frequently result in just the type of skipping that you describe.
If you still want to replace the derailleur, then just about any cheap one will do - it doesn't have to be specified as for 5 cogs since the derailleur doesn't really care about the number of them. But indexed shifters do care about the number and spacing of the cogs - so replacing your current friction shifters with new indexed ones would also require other components to be replaced and is unlikely to be worthwhile.
Here's a reasonably cheap derailleur that should work better than the old Huret you probably have now (but again, I doubt that this is your problem):
http://www.nashbar.com/bikes/Product...200545__202435