I am in the process of upgrading my road bike from 3x9 Sora FD/Tiagra RD with Sora shifters to 3x9 105 FD/RD. Any suggestions on shifter upgrades? Derailleurs have been replaced, have new SRAM 9spd cassette and chain, all work OK, but would like different shifters to finish improvements. Would any newer 105/Ultegra/Dura-Ace be compatible, or should I focus on a hunt for a decent used set?
Current 105/Ultegra/Dura-ace are more than 9 speed, so you can't use them. Plus, the old 105 or tiagra 9 speed shifters you'll get are probably the same as the current Sora shifters anyway, due to trickle down technology (just with tiny modifications and a price premium).
So, in short, if you're sticking with 9 speed, don't bother -- you'll just pay more for a different sticker on the shifters.
If it were me, part of any upgrade would involve addressing the question of future-proofing the bike, for example so that parts going forward are easier to obtain.
I'm afraid that, in your case, this means I would be looking at going beyond 9-speed.
You mention 105/Ultegra and Dura Ace - well, these are all now 11-speed setups so straight away you're looking at hunting through back catalogues to source 9-speed parts in these groups. Unfortunately in Shimano's world, anything currently 9-speed is at the lower end of the spectrum, in terms of quality.
You will still find plenty of 10-speed parts at the moment, but again, and with the exception of Tiagra, these are "old" in terms of Shimano's current range.
Another observation is that triples seem to be nowhere near as common as they used to be, lots of groups bypassing them in favour of compact doubles.
For what it's worth, I have a 3x9 bike (Tiagra mostly, from around 5 years ago) and every time I think of upgrading it, I put that project on the back burner. Quite simply it would be too much faff for not enough gain. I think my favoured upgrade path would be to go for a 3x10 105 group, with a view to then swapping in 6600 or 6700 (10-speed Ultegra) parts as things wore out. But that;s just a personal thing and, as I say, I have no appetite for that project just yet.
All newer 105/Ultegra/Dura-Ace are 11 speed, so they would not be compatible with your 9 speed derailleur. I believe you'll have to find some old ST-5500 levers if you want 9 speed 105. The current generation is 5800, so that's 3 generations old.
I agree with @Batman, that it probably makes sense to go with current generation 9 speed shifters. Even the 5500 shifters have the cable going out the side, which is the major complaint with sub-105 level components. The current 3400 level 9 speed Sora looks to have the thumb actuated downshift, which some people don't like, and the 5500 looks like it uses the extra lever behind the brake lever. The 3500 level 9 speed Sora uses a lever for downshifting. If this is a big concern for you, choose appropriately.