I just did exactly this. There is now ten miles a week of walking in my commute. I wore out three pairs of shoes before spending a bit more for some Doc Martens; they meet exactly this requirement. Not too heavy for "city" walking, although a bit heavier than trainers. No problem in the wet. Durable. The only reason I wouldn't go hillwalking in them is wanting to keep them clean.

(This is almost literally the "Vimes boots theory of poverty" from Pratchett)