When you play that squad, you always choose that time traveler. What made this combination so good?

Rusting Hulks: this one is obvious: Camila, since the battlefield will be covered in smoke and she's immune to it.
Zenith Guard / Hazardous Mechs: Abe, he takes one less point of self-damage since he's armored.
Blitzkrieg / Steel Judoka: I feel they lack attack options, so, for me, Harold or Kazaaakpleth are the way to go (you can "repair' even at full health)
Frozen Titans: Archimedes in a powered prime can do both offense and defense in the same turn. (I heard that the ranged won't get frozen with Bethany's or Mafan's shield, but it doesn't suit my play-style).

I always just go with Camilla. It's not as much for the smoke immunity as for the webbing immunity. That's highly useful regardless of which squad I'm playing with or which island I'm defending, since just about every mission has at least one web shooter (and, often, many more than just one). I used to put her in my Prime mech, since that tends to do the most damage, but I've recently switched to putting her in my Ranged mech, since Ranged mechs can't fire at a unit that's right next to them. The other mech classes can usually counter the webbing in some way, by attacking the Vek, pushing it away or leaping/flying out of danger. Putting Camilla in the Ranged mech prevents it from getting caught in a situation that it can't get out of.

Anyways, every time that I start a new timeline, Camilla is the pilot that I keep. At the moment, I've completed about 10 timelines with her. Before that, I had completed at least 5 when I screwed up and got her killed... which was so heartbreaking that I actually entertained the idea of calling it quits. Luckily, though, after a couple more timelines, I received her again and have been even more careful with her this time.

Yeah, I also like Camilla. You're aware you can change your time traveler at the start of a new playthrough, aren't you?

Oh, and I changed my mind about Bethany and the Frozen Titans... she's the real deal.

You know, I've seen that option and just never clicked on it, perhaps afraid that I'd lose the option of selecting Camilla. Can you really select any time traveler? If so, what's the point of choosing one to keep when you save a timeline? Oh, maybe it's that you get to keep that time traveler's experience and skills and, if you select him or her at the start of the new play-through, you have work them up from zero again. If so, then I guess that I can afford to lose Camilla more than I thought. I'll have to try it out. Thanks for the tip.

Yep.

There are versions of Camilla, the best one is Camilla with +2 HP and +1 move

I wasn't aware that there were multiple versions of pilots. The only Camilla that I've had has Evasion, +1 Mech Reactor and +1 Move. I think that that's better than the version that you mentioned, since you could always put that 1 reactor core into +2 HP right at the start. Of course, you lose the option later to increase the HP to 7, but I find 7 HP to be overkill most of the time. 5 HP seems to be enough for all but the mechs whose weapons deal self damage, but there aren't too many of those.

Camilla will always have evasion but the other two skills will be random. I think +1 mech reactor is also good, you can move further early on but with limited HP. With 5 HP, her life is quite safe from the start. A reactor core is easy to get so I prefer to err... 'embiggen'.. her health capacity.

Hazardous Mechs + Abe Isamu is an obvious choice.
Silica + Combat Mech is quite powerful when you upgrade your weapon to Dash.