I know how you feel -- I never learned how to cook and only recently started buying fresh produce instead of prepackaged stuff! It's amazing how much it's cut my grocery bill, too.
Here are a few suggestions:
Buy more veggies! You've only got one (carrots) on that list. They're important because fruits are mostly fructose, water and fiber, which never really fill me up (except for bananas). Veggies can be hard to figure out how to eat and cook, if you're like me... I learned some great, simple recipes for stuff like kale and beets on
Planet Organics. It's a San Francisco company that delivers fresh, local produce to your door every or every other week. I subscribed to the service for a few months and it really helped me learn how to cook new vegetables. Now kale and beets are some of my favorites! Most areas have a similar service if you're interested. Just Google "produce delivery."
Also, I've been on a big mushroom fix lately. They taste really, really good when you're craving something meaty but don't want any meat, and they're super easy to cook (or eat raw). There are also about a million different kinds. I'm lazy, and have been tossing creminis in a skillet with olive oil and frozen, prepared packages of veggies (chopped onion, bell pepper strips, sliced zuchini) and jarred, minced garlic and ginger. That's a fun way to experiment with spices, but the cool thing about fresh produce is that it doesn't really need a lot added to taste really good.
And get yourself a couple potatos and a potato masher. White potatos are a high-GI item, so they can make you hungry if you don't eat them with lots of veggies and low-GI items, but it's super easy to wash a potato, boil it, drain it, add some milk (or soy milk) and olive oil (or butter/margarine), mash it with the masher (integral!! forks don't work very well for potato mashing) and mix some steamed veggies in with it. I don't buy the bags of potatos anymore becuase they always sprout before I get the chance to eat them. Oh, another great potato recipe -- cut them into wedges, toss them in a ziplock baggie with two tablespoons of a mix of olive oil, lemon juice, pepper, cumin, salt, and a pinch of sugar, and bake them. Tastes great with salsa.
Here's a link about storing produce:
How should I store Produce?
A lot of stuff you can leave out for a short time, refrigerate for a longer time, and freeze for a very long time.
One thing I do with bananas is leave them out when they're partially ripened because I like the tangy taste of a fresh banana. Then, when the skin turns black and they start to ripen, I peel them and stick them in the freezer. My boyfriend loves frozen ripe bananas more than ice cream. If you bake, you can wait until the bananas are all black on the outside and make banana bread with them.
Sorry for rambling, this is something I've been trying to figure out lately too. I'm starting to think that the biggest plus of going vegetarian isn't so much cutting out meat but being forced to eat more veggies, something that too many people just don't get enough of (me included).