Just my 2penn'orth...
I've used Karrimor weathertite lightweight walking boots , on & off bike, for several years: They usually cost about £30 in Sports direct & would give me 12 months of dry feet before leaking - But...
The last 2 pairs have leaked within weeks of buying, so I've upgraded to Karrimor ksb (Nevis I think) which are £50 (1/2 rrp) & e-vent lined: This is regarded as equal in performance to Goretex, so should give 2 to 3 years' protection if my experience is typical.
They come up to the ankle, with a bellows tongue & so far have kept out everything thrown at them.
One point to note is that they have Vibram heavily cleated soles, so I've chucked out my rat-traps (old fashioned, I know) as I couldn't get my tootsies down quick enough & went base-over-apex when stopping at traffic lights.
Regarding capes - I keep one in the pannizr, so I can get it on quick when there's a sudden dowser, but get it hitched-up on my backpack; so I superglued the weight from one of those vzrtical blinds in the bottom back, so I can fling it over the rucsack easier. A couple of feet of knicker elastic in a loop (slipped over the saddle horn) stops the back flying up in a tailwind.