I like the glass. You are right about having too many lines. You can spot-clean going up with the window-cleaner, stash it upstairs, then do the same later going down.

What about a solid fill in? Plywood is fashionable.

There might be a removable coating you could have put on the glass to make fingerprints less obvious. Peel off once the children are older.

Glass all the way. As the children grow older, the chore of cleaning it can be delegated...

Maintenance of glazed balustrades can be a problem...The black metal baluster option works well with the style of the stair - however if you choose this option, our recommendation would be to leave out the decorative bits - keep it simple.

I like glass: it makes the room look modern and spacious and bright. But I can certainly understand your worries about keeping it spotless. (Glass only looks nice if it's clean.)
If you are worried about "too many lines" would changing the changing the colour of the iron to something more subtle be an option for you? I agree with Matthews about keeping the balustrade simple and leave out the ornament.
The other thought I had was that your staircase has open steps. I find it more constistant to keep the railing open as well instead of closing it up on one side.

I would go for the glass, but I hear you on keeping it clean! We have a timber hand rail with horizontal wires, which leaves things open. Our young kids use the wall more as they can't yet reach the hand rail, so I am forever cleaning the wall instead, haha....