I love the strider plus too! Am really happy with it as a single - love the size of the shopping basket as BlueSky mentioned, as we walk to the shops a couple of times a week.

It is stable but you can't put a nappy bag over the handles.
I put the nappy bag on the handles and its fine. Although I noticed, it does slide right down when the seat is reverse facing, as it doesn't have the hood to stop it sliding down. The way round this is to buy hooks/clips that you fasten onto the handles (mine velcro on) and then you just hang the nappy bag of these - works a treat.

I also have the Maclarent Vogue, which doesn't have adjustable handles but the handles are taller than other umbrella strollers. It has 3 seat positions, one is completly flat so suitable for nb's. DD sleeps ok in it, although she was sleeping in it when we were at my brothers the other night, and because her legs now hang over the edge of the seat, we think she got cramp as she woke up screaming and shaking her legs. I put the nappy bag over the handles, which is still pretty stable with a 12kg toddler in it but as soon as you add another bag of shopping or something, when you take the toddler out, it tips backward.