I am new to this site and looking to lose some serious weight. I know all about eating 3 meals a day and small snacks inbetween. I'm a stay a home mom and we're on a budget.
What are the best "diet plans" for staying within my budget?

We dont really go in for "diet plans" much around here. We tend to go in for eating really healthily combined with regular exercise.

You have found your way to the nutrition section. I suggest that you read the sticky threads. They give all sorts of information about the different nutrients that our bodies will thank us for using as fuel. Also the optimal proportions for us to have those nutrients for not only weight loss but also good health.

We then invent our own "diet plan" which is just that we select food in much the same way as we have always done - but now we make an informed choice.

We generally go in for cooking food from scratch which tends to be cheaper than buying food in boxes anyway.

We log our food through a free account in FitDay - Free Weight Loss and Diet Journal or similar which not only counts calories but all the other nutrients too. It tends to be a bit of a game of trial and error at first as you key the stuff in and see how it compares to the nutritional targets that you were shooting for.

In order to give you a head start the following foods all feature in my shopping basket and go to form my "diet plan". You can naturally select your own.
- plenty of fruit and vegetables
- lean meat, fish, poultry - (skinless)
- eggs, quorn, quark, fat free dairy, low fat dairy, skimmed milk
- beans
- fry light spray for stir frying
- olive spread
- were I to have bread, pasta or rice I would choose wholemeal
- when I have cereal I have the kind with no sugar
- granulated sweetener

What Omega said.

The "diet plan" that I follow is eating reasonable amounts of fresh healthy food. That's it. And in fact, doing so costs me less than it did when I bought packaged foods, ate junk, ate fast food, etc.

Lots of fruit and veg, lean meat, complex carbs, and healthy fats. Make sure you're measuring/weighing your food so that you're really eating single servings.

And, of course, exercise. Walk, run, do bodyweight exercises like squats, pushups, lunges, etc.