Well, flying economy it's tricky.
It depends on the actual booking classes.
If it's cheap classes you may be best off with UA MP , even if you never fly them, as they tend do give 100% miles for most booking classes.
BMI DC, though in principle looking nice, oftentimes only gives 25-50% of flown miles for TK and LH flights.
TK M&S will at least give full credit for TK flights and also for many LH classes.
TG has booking classes that give miles nowhere.

You can join every FF program you like. And better do it for the carriers you fly at least (and maybe a few more).
Crediting flights you've already taken may work (or not), depending on program. Chances are that you can get credit for flights maybe a month or 3 back with the program of the airline flown (YMMV ).
Once you joined a program you can expect that you can credit flights dating back several months even if your number was not in the booking.