OP: I have the same criteria and - after some sporadic research - I'm leaning toward the plastic half-shed. Down the road, we might go for a more attractive outdoor shed and re-purpose the plastic shed for holding cleaning supplies, etc. in the laundry room.

You may not need a full-on shed - maybe just a plastic half-height shed that would hold the mower and a few other small things. Something like this:
http://www.wayfair.com/Keter-Woodland-4.42-W-x-25-D-Resin-Tool-Shed-211166-KTR1063.html

We have a new house with very limited yard space, and need a shed to place our lawnmower and just a few other yard items. There is no garage. The shed does not need to be huge.

Can anyone recommend a relatively attractive, but good value shed option? I would like it to fit on a side of the house which has only 8 feet or 10 feet to the property line.