I loved Fibertrends 'Fabulous Felted Totes' pattern. It's not a freebie, but believe the cost was about $5 and the pattern has three sizes of totes to knit. It's super simple as the bottom is knit in the round too, no stitches to pick up. When finished felting you shape it to get the bottom flat.
The Booga Bag pattern is very easy too, but you do make the bottom separately and pick up the stitches before knitting in the round. And it's free. http://www.blacksheepbags.com/booga_bag.html
It's rather small though for what you're wanting it for.
When I first started knitting I bought the Two Old Bags, bag pattern and couldn't make sense of it either. Thankfully I didn't stress too much over it as our new puppy took a liking to it and shredded it!