The TOS novel The Final Reflection does a nice riff on the TOS transporter effect, and how the Klingons are all recoiling at the horrible noise it makes.
As much as I'm an old-school TOS fan, I went with the TNG series as it's a great improvement on the original while still retaining the general feel of it. While I wanted to like TMP effect when I first saw it, but it just seemed so cheesy for a multi-million dollar production; almost like it was painted on. I always got the impression it was only meant to be seen while in the transporter leaving the unanswered question of what it would look like when someone actually beamed up or down on a planet. Was the tube still there or not? While I image having someone transport up or down somewhere was never meant to be a quiet, clandestine event, but the TWOK-TUC effect always seemed like it would be a noisy, obvious affair, equivalent to firecrackers going off in the room and would certainly cut down on a tactical advantage if one didn't want someone to know they were coming. This goes for the Klingon transporter as well since it was just a tweak on the Star Fleet effect and I can't image that people appearing and disappearing in a big light show in the middle of Golden Gate Park would go unnoticed. VOY was ok, but is merely just a variation on a theme without actually improving it, as pretty much of the rest as well.
Favorite to me means it has to be one. I'm a sucker for big budget productions and effects so I have to say my favorite Transporter Beam effect is what I saw in "Into Darkness". What is captivating about it is how the energy pattern swirls around the body and transforms into energy particles*, the surround sound also builds the moment as well. What comes close if I had to choose was what was done in TMP, again I felt was an advancement to what was done in TOS. TWOK -TUC transporter beam looked cheap to me and as I've mentioned in other threads I believe the popularity of that effect and everything else including the Monster Maroons was because of the huge success from TWOK. In TOS there was a sense the Transporter was advancing where it didn't take as much time to power up the tech other than complications. This is what was seen tragically in TMP, but I felt by the time TWOK era happened I would see the tech advance to the point I could see crew members didn't have to stand at a point to beam up. Strange, I saw something I found interesting in TVH where Spock walks as he beams but this was on a Klingon vessel and not a Federation vessel. JJ Abrams two movies lived up to my expectations of the transporter twice fold and I only expect it to get better after; for me that's the bar. * Snap crackle pop, appeared to be a snide.
I always had a problem with people talking during transport, as in Trek II. You shouldn't be able to do that. I was never a fan of people being able to leap into an active transport in progress, like in Trek IV. They should have had some kind of exclusion field around the person beaming. They seemed to play fast and loose with that idea. I liked the TNG effect. It felt like a mature, standard technology.
That almost looked mystical. Helical as I remember? Having a double helix field that replicates itself down to an individual cell-sparkle based on embryo development might be interesting…