I used to live car free in woods hole every summer. I tried 3 approaches, grocery panniers, touring panniers and a kiddie trailer.

I didn't like grocery panniers, they just don't hold that much. Touring panniers work just fine, you just need to repack your groceries, and of course you are limited by their volume, but it sounds like you don't want to carry that much per trip (and you could use both front and rear ones). I got mine at LLbean and they were fine. I think this is the best option for you, and you can also use them on a tour.

I bought the kiddie trailer used, even though my kids were grown, and found this the best to carry lots of stuff (water, laundry detergent, laundry). BUT the one problem is that if the stuff was too heavy it would drag on the bottom. So, if you are gonna go the trailer route, I'd get a trailer designed fro carrying stuff not kids. I know you said you aren't interested in a trailer, but thought I'd post my comparisons for the record in case someone else reads this with a similar question.