I have a "primary" airline, which is the one where I'm trying to keep or get Elite status. That airline gets first priority but I can use others if:

1. Schedule is more convenient.
2. Price is substantially better (not a difference of $50 but of $200+)
3. I can avoid connections at an airport I hate (LHR comes to mind)

Aircraft isn't a big consideration for me.
I'm a little wary of airlines in shaky financial condition- mostly because I don't want them pulling the plug on their flights unexpectedly. I feel the same about those with possible labor problems.

In considering which airline I want to get or keep Elite status, I consider their availability on routes I'm likely to fly, how well they treat low-tier Elites (I'm never going to be a 100,000+ mile flier) and the quality of their Coach product, which is where I spend most of my time and all of my personal travel. This, for example, currently knocks out one airline where if my very tall husband gets an aisle seat on transatlantics, I'm stuck with a middle seat because their aircraft don't have a side with only a on one side of the plane.