I chose lenses for distance. I don't think it even occurred to me to have lenses for reading as I have always worn glasses. I also think I had a little astigmatism which, if I recall correctly, may have affected my decision.
Sorry to be so vague, but this was 4 years ago and I can't honestly remember everything that affected my decisions. One thing for sure was that I always wanted photochromic glasses as the sun here is so bright and I like it when they go dark!
An Australian friend of mine has varifocal lenses but I decided against.
Distance vision is still perfect. Street signs are OK and when I look down through the bottom of my glasses, I can focus on things close up. I automatically look through the correct part of the lens to get close up objects in focus. e.g. right now the keyboard is in focus, the computer screen is, and I can look over the top of the glasses to watch the F1 qualifying!
If anything, I would change the varifocal glasses so that more of the glass at the top of each lens was plain glass, i.e. no prescription at all. The ones I have now - the only ones I have had - do have a slight effect on the distance vision, so I often look over the top, avoiding the glasses altogether.
I don't believe my "depth perception" has been affected, but not 100% sure what that is!