I keep debating a trailer, but I live in an urban area where I can and do make use of buses. A trailer would be a handicap for me most of the time. I can't take it on the bus very well like a bicycle which goes onto the front carrier.
I have a set of the "M-Wave Double Day Tripper Bicycle Pannier" bags (under $30 on amazon) and they hold a ton of stuff. They aren't super heavy duty in some places, or maybe I'm just rough with them since I was taking them back off a lot when I used them regularly when I was in AZ in Dec and Jan and used them on my bikes for shopping runs. The bikes stayed outside and I didn't want the bags exposed to beating sunshine everyday when not in use.
You need a somewhat robust rack if you really load them down with weight. I put a flimsy rack on my LeTour (Wal-Mart site to store, about $14, last year) and it gets wobbly when the bags are loaded with heavy groceries, but not so much so that I couldn't ride it. The rack didn't fail, however despite the wobble.
On my cheap China-made mountain bike I got from a pawn shop brand new for $50, I put a more sturdy rack I ended up getting in-store at a Wal-Mart in AZ and it doesn't have the wobble problem.
I need to go back and switch the racks since I think the Le Tour is better for urban use here. I do like having more traction with the mountain bike tires, but it's a heavier bike and doesn't have as many gears. Plus I can't seem to get it adjusted right either and it likes to skip over one of the gears most of the time. Just cheaply made but it served me well for off-road riding some in AZ and gives me a decent back-up bike should something go wrong with my LeTour.