The best way for fragile champions to stay alive is ... to not be hit :)

So the answer to your question is: none of the above.

And those gears for what kind of champions are?

I'm not sure I understand your question. Are you asking what gear champs like Arbiter should be wearing? If so, the answer is: speed, and nothing else. Pure support champs like Arb have no need for any other stat.

Thank you. So Divine speed is the best for her?

You explained very well what kind o champs need speed sets.

Can you explain to me also, what kind of champs need the sets that I have given above (those who preserve or gain HP)?

The short answer to your question is - stop thinking about sets. I'm doubtful that you're at a point in the game where the bonuses from sets will outweigh the likely sub-par items you'll have to use to get them.

Focus on making sure the items have the correct stats for the champs you're using them on. That means no flat-stat glove/chest, only SPD boots, CRATE or CDMG gloves for DPS champs, and ideally no flat substats either, though you can tolerate one or two as long as they aren't upgraded.

What are the DPS champs?

I don't know. That's a you question. I don't know your roster.

That means that they are my usual fighting champions, and DPS is a abbreviation by initials from D... P... S...?

DPS is a term that is used commonly in RPGs. Technically it stands for "Damage per Second", but practically speaking it refers to someone whose role is primarily to do damage.

In this game, that tends to come in two forms - either direct damage (often called "face damage"), IE with big damage abilities - your starter champs (Kael, etc) fall into this bracket, and there are quite a few others of course. Or, longer-term damage abilities (often referred to as DOTs, or "Damage over Time"). Sometimes, people can be both - Kael for example has a big damage ability on his A2, and lots of long-term damage from the poisons on his A1 and A3.

A1, A2 and A3 meaning his skill in up > down order, as I presume. 

Thank you a lot. 

Now you gave me a clue to escape from analytical view to intuitive approach. 

I wish you to have, now and forever, the time of your life!