Moving forward I want to use just one yeast (for now at least) for strong cider, cyser, and apple wine.
If you had to choose just one yourselves what would it be?
I'm thinking 71B?
Choose your yeast like you would choose a tool, you don't use a screwdriver when the job calls for a hammer. For the things you mentioned, you'll need a wine yeast of some sort. 71-B will metabolize approx. 20% of the malic acid in your juice, thereby "softening" your apple wine/cider/cyser/etc...
Malic acid is 1 of the compounds that make an apple taste like an apple, not enough malic & your cider/wine could end up tasting more like a wet dishrag. Sometimes though, malic reduction is exactly what you want, say, in a crab apple cider where it's too acidic to taste good.
Some yeasts are better at lower temps than others, some yeasts are better for sweeter wines & some will ferment out dry as slate; it all depends on the recipe & what you want for an end product. I would never use a wine yeast to make cider, as wine yeasts tend to strip out a lot of flavor & will take juice dry without added sugar. I use ale yeast (usually Nottingham) for cider because it gives me the best end product. I use wine yeast for wine & cyser as ale yeast simply won't ferment out to a high enough ABV, as it's alcohol tolerance is much lower than wine yeast. Some yeast strains are better for some things than others, you probably wouldn't like a Chianti that was made with a Riesling yeast strain. Have a look at the different qualities & intended uses for various strains here:
http://www.lallemandbrewing.com/products/
Not sure of your location, but I would think there's a homebrew supply shop reasonably nearby, if not, you can always order yeast online. Obviously, it's up to you as to what strain(s) of yeast you use, but I'd say don't limit yourself to just 1 strain; one size doesn't fit all when it comes to yeast strains.
Regards, GF.