To Garden or Not to Garden...???

I've been debating doing a garden in our backyard but...I don't have any idea where to start. I'm a little city girl at heart :) And those that know me are now laughing because I grew up in a town that is only about 50,000 people or so....I know not big but pretty big for Arkansas.

Here are a couple of questions I've been throwing around...
Do I till up a plot or just do a raised garden out of landscape timber and top soil? I'm going more towards the raised garden on this.

Would it be worth the time and money since we don't eat alot of veggies?

Here are the veggies we eat...
Corn
Mashed Potatoes and hashbrowns (I could prepare and freeze the hashbrowns)
Tomatoes for tomato sauce (would it be ok to freeze for a yr or so?)
Purple Hull Peas

Fruit...
Strawberries and Blackberries
Apples
Bananas
Oranges

Bananas and Oranges would definitely be out b/c of our climate but hum I wonder about an Apple tree...the kids would love that.

Also when do you start planting????

See I told you I was a little city girl that doesn't have a clue!!!!!!!!!!!!! I'm trying to save and cut out as much as possible but don't know if this would be cost effective or not. I'm sure it probably would but want others opinions. HELP!