My current rope "quiver:"

Two big beefy 60M non-dry 11mm ropes for top roping at the crag - they can stand all kinds of abuse and never shows any sign of wear. We often head out with families for a day on the ropes and these are awesome for that.

One 60M 10mm dry-treated rope that's good for leading, glacier travel, ice climbing and alpine climbing.

Two 60M dry treated 8.6mm half ropes - can be used on it's own as a nice glacier travel rope, together for alpine/ice leading - very versatile.

Two 30M 8mm "Rando" ropes - A great alternative to a 60M half rope as you can split the carrying duties. We often carry both for a team of three on a glacier where the climbing won't involve placing much gear or the possibility of lead falls.

If I had to only own ONE rope? Whoa, what a hard decision. I'd probably go for a 60M or 70M 10mm-ish dry treated single rope. This size of rope ain't super light like an 8mm dental-floss, but it's so versatile. You can take it rock or ice climbing (though days of top roping on it might not be the best) trudge over glaciers with four people on it easily, use it alpine climbing - it does most anything. It's cheaper than two half ropes and does more stuff than two 8mm Rando ropes. A 10mm also takes prussiks easily and won't fly through a rap device when you go past the half-way point like a <9mm will. (But that doesn't mean you don't back up your raps, just sayin...)