My errand setup is very similar. Rear rack, open top grocery panniers. Best solution I've found for my needs.

I have a Bontrager BackRack S on my compact frame hybrid with sloping downtube. But there are plenty of good similarly priced racks around. I like the tube support attached to the seat stay better than some of the twisty flat spring supports on other racks.

And I use the Nashbar Townie panniers, nearly identical to the Banjo Bros, JandD, and a few other models. Some have mesh sides, some solid ballistic nylon fabric; some have slightly different attachment methods -- usually hooks over the rack and a bungee hook for the bottom eyelet; but all work pretty much the same way. They fold flat when not in use and don't add much wind resistance. So some days I'll take a 20-40 mile ride with the empty panniers, then stop for groceries on the way home.

I also have a huge soft sided rolling drink cart that's good for errands when I need to fetch lots of stuff that needs to be kept cold or frozen, but it's a bit of a hassle to rig up. Generally I'll use heavy duty zip ties reinforced with bungee cords. And I have a heavy duty milk crate, but it's a real hassle to use -- I'd use it only for lugging awkward loads.

If I had room in my apartment I'd get a cruiser as a dedicated errand bike and rig it up with Wald folding baskets on the rear and a big basket on the front. It'd be much easier for my errands, which range from a mile round trip to 10 miles, tops.