We have the hanging original globe fixtures and with the loss of incandescent bulbs what is the best solution. Should we go for LED, Halogen or Florescent bulbs? Will these work on a rheostat?
Note that 150 watt incandescent bulbs are still available because there's no substitute technology - I recently picked up clear 150w bulbs at Orchard. I've never used them in the past, but I suspect they'll do better in the enclosed fixtures.
Switch makes the only LED light bulbs, I know of, that can be used inside closed fixtures. They are available in sizes up to 100W equivalent. They are not cheap but cost less than a broken globe. So far they have worked with all of the dimmers we have tried, but LED bulbs are not guaranteed for all dimmers and some combinations will cause problems. New dimmers often cost less than the bulb.
I would not use any other LED bulbs in your globe fixtures. Most specifically warn against use in closed fixtures and, working on LED fixture design as my day job, I would tend to agree with them. The increased temperature in an enclosed fixture will cause very short bulb lifetime.
Compact fluorescents have similar issues inside enclosed fixtures. While the fluorescent lighting tube is more robust than an LED, the ballast electronics are not and show vastly reduced lifetime inside an enclosed fixture.
Which leaves incandescents that are hot and inefficient and have a naturally short lifetime and are disappearing off the shelves.
Our solution has been to replace the lights with Switch brand bulbs as they burn out. We have a Switch 75 that has been running for over a year on a dimmer without problem. There is a Switch 100 in the living room, also on a dimmer, that has been going for several months.
I still have my fingers crossed for more alternatives.
Xledia makes a line of LEDs which are recommended for fully enclosed fixtures. They're available on Amazon. A soft white (2700K) 75w equivalent (uses 13W) is about $35. They are not dimmable.
I haven't tried them yet but I have a few on order and I'll let you know how they work out.