Very large (22 litre) saddlebag, resting on the rear rack... currently a Highlander haversack with some correx board in it and some extra cam buckle straps doing a Carradice impersonation... or sometimes a no-name satchel as a smaller version (10 litre) of the same. Hiking rain cover over it when needed.
I use roll-up-able double panniers (Basil Mara) when I'm bringing lots of shopping home - they strap onto the bag until needed, but will unfurl and strap on to carry about two shopping bags each side. Waterproofish, if you know what I mean. If it's just a little more shopping than the rear bag will accept, it goes into the front mini basket.
All my bikes have rear racks. They don't slow you down much. Big panniers can a bit, especially in fen headwinds, hence why I like my roll-up-able ones.
As for the suboptimal past attempts: Even when I used a rucksack (some Eurotrek 13 litre one for about a decade), it used to get strapped to the rear rack because I don't like a sweaty back, but they're not designed for it, so it was a bit faffy (tying straps up to keep them from catching spokes) and eventually wore through from shuffling against the rack rails. The Alpkit dry bag (aka canoe bag) was better and still gets used sometimes, but is less good as a bag (only having a roll-top opening is a bit annoying) and it also started to wear through (patched but I don't really trust it any more). I've also a trunk bag with fold-down panniers, but maybe the one I got was poor because the side panniers only held one shopping bag each, one side pannier started to come away, the top was always a bit floppy side-to-side and it was a bit annoying to attach and detach the velcro. I've also used a rear crate but that's annoyingly big and stuff seems to rattle in it whenever possible.
My, I've had a lot of goes at this, haven't I?
