My current lunch bag, I got at Wal-Mart several years ago, back in the camping dept. Has a long shoulder strap, big, solid plastic liner, 3 outer pockets, extra storage in zipper lid! Love that thing!
Pick up a few of those icey things you can toss in the freezer, take one, freeze one, so you always have a cold one, and you're good to go!
For the record, this lunch box would hold a 12 pack of beer bottles, so plenty big enough! Solid, lots of storage! I pack my breakfast, snacks and lunch. No problem.