The best Leica made LTM camera (and arguably the most mechanically refined M39 camera ever) was the IIIg IMO. It has a look and feel that just exudes quality and excellence -- reminiscent of the very early Leica M3's.
The IIIf, as noted above, is certainly a contender for over-the-top excellence as well. The IIIf's are often well-worn little beasts for very good reasons, while the (few) IIIg's I've seen have been lightly used (if at all). I expect the IIIg was not adopted in its era so much by pros - perhaps it was too pricey or bypassed in favor of its famous contemporary the operationally superior M2/M3 by those needing a rangefinder. That is good for us now though!
Even the straight III is excellent - a hand made 1930's gem.
I am also partial to the II series, e.g. the IIf. They are wonderful and super reliable so long as you can forgo slow speeds. All early Leica's are in a class beyond anything made in the FSU.
Canon L1, Leotax S, Bessa R2C, Konica Autoreflex, Canon FX, Pentax Spotmatic, Minolta SRT-101, Nikon F, Exakta VX, Miranda Automex II, Leotax K3, Yashica Mat LM, Leotax S, Pen FT, Rollei 35S, Ricoh Singlex TLS, Kowa Six, Pentax K1000, Canonflex, Praktina, Voigtlander R2C