Machamp, Arcanine or Rhydon?

Machamp.

Definitely not Arcanine.

Probably Rhydon or Machamp, and I'd go Rhydon because MS/E Rhydon is a great moveset against Raid Bosses given the current lineup.

First Machamp, then Rhydon.

Machamp then Rhydon when you can. With Arcanine I would want to go for WC and get a fun new defender.

Champ, only Champ.

Machamp

go for machamp, a c/dp one is actually a really good attacker

Machamp for sure. It is currently the most valued attacker right now, being strong against the 3 raid bosses that are arguably the most desirable - Snorlax, Lapras and Tyranitar.

Your fast TM will guarantee the strongest moveset against those Pokemon.

Also, the difference in usefulness between the potential new moveset and the current one is highest with your Machamp.

Rhydon is still great with Rock Smash with the buff to super effectiveness it is actually better than Mud Slap in some cases e.g. Tyranitar and Snorlax, while Bullet Punch is pretty much always inferior to Counter.

Arcanine is kind of meh, not worth it. For raids, Flareon does more damage and that's what's most important rather than timing out in my opinion. Not having enough damage happens more often than having all 6 Pokemon faint in my experience.

Definitely Machamp, even though its probably over a year away Rhydon does evolve and that would just be a waste of a TM in the end.