Which is most important to TM

They are all equally important because these are all the moves that everyone uses TMs on to get STAB. Well except for the Bite Gyrados and WP Vaporeon......Those moves already have STAB and Bite is already a good move on Gyrados.

SW:
No, protects weaknesses at defense. Yes if it is an attacker.

IT:
Same as SW.

Bite:
No unless you want defense. It has the dark coverage and a short cooldown time.

BP:
Same as SW.

HB:
Change, not the best move on both.

FB:
Same as SW, but FB doesn't protects most weaknesses.

WP:
Change, the worst charge move for Vaporeon on both.

MH:
Same as SW.

HS:
Same as SW.

Quick moves:
3. NO

3, 4. First priority, 3 or 4, depending which is bigger or will get bigger sooner.
1: latest priority, Dragonite is top only vs. Jolteon, for others trails behind the ones with single or double supper effectiveness.

Charge moves:
2, 3. Tyra or Machamp, since either one of the options is very very good, again basedon which one is bigger or will get bigger. Also Machamp best vs, lvl 4, Tyra among the best vs. lvl 3 raid bosess if you solo.
4. Rhydon if you want to solo or deal max damage vs. Fire bosses
3. Vape if you don;t have another maxed one with HP or AT. Excelent vs. Fire bosses and Top vs. Rhydon lvl 4 boss.
1. Dragonite, see above, HU excellent vs Machamp, OU excellent vs. Jolteon. Both good vs. Alakazam, to complete your Tyras (or Gengars if FB one) army. Of course only if already or close to being maxed for your level. Otherwise NO.

In the current meta TMs should only be used to get STAB moves that are SE into defenders that is the best to counter against including the upcoming Legendaries.

Rankings
Quick moves:
1: IT to B Tyranitar - Best or top Counter to a lot of Legendaries especially Mewtwo

2: BP to C Machamp - Best or top Counter to the top three Raid Bosses (Tyranitar, Snorlax, and Lapras). It's a Larvitar Candy farmer.

3: SW to DT Dragonite - Best generalist counter to a lot of raid bosses.

4: B to DT Gyarados - who cares. Gyarados has become less relevant after gym rework

Charge moves:
1: FB to C or SE Tyranitar - need C or SE against Raid bosses especially legendaries.

2: MH to SE or EQ Rhydon - top ground type counter to Electric and Fire raid bosses, and legendary birds especially Zapdos.

3: HS to DP or CC Machamp - larvitar candy farmer

4: HB to H or O Dragonite - HB on Dnites is a sin

5: WP to HP or AT Vaporeon - Machamp back up against Tyranitars.

All except Gyarados, Rhydon and Vaporeon
.
Be sure to wait with using TMS until the pokemon is ready to use (p.ex. if it is level 20 and you are willing to spend 80 candy and 80k dust)

If it is not ready, you could instead do another raid and try to get a better Tyranitar, Rhydon, Vaporeon or Machamp and safe your valuable Machines.

TOP 1- Get C/ DP Machamp and B/C Tyranitar
TOP 2- Best moves on Top DPS like Flareon