When just beginning some preps, stay away from freeze dried foods. In an emergency you need calories and if you look at the labels of some, they provide as little as 100 calories per serving, yet the pouch tells you there are 4 servings! That is not enough and is expensive per calorie.

Many good points have been posted so far. One thing I tell people is decide what situation you are prepping for. I am not focused on TEOTWAWKI preps, but on getting by for a bad SHTF situation that might last up to a year. We began with a focus on three days of no gas, water or electricity due to an earthquake. Actually we have dealt with 3 days of no electricity due to wind damage so that provided a slight trial run.

Water storage is critical. There is a rule of threes. Three minutes without oxygen, three days without water and 3 days without food and you are out of the game forever. Given that it we need that water let's look at how to begin storage for next to nothing as that was the question of the OP (original poster.)

Get your hands on some 2 liter soda bottles. We do not drink much but on occasion we have a family party and someone brings a few bottles of coke or whatever. Rinse them very well and refill with tap water. Add about 6 drops of unscented household bleach, put the cap on tightly and store in the corner of a closet or other fairly cool area. I like to use a permanent marker to put the date on the bottle. The "experts" say it is good for a year, though I tend to empty and refill about every 6 months. Pour the water on your plants, not down the drain. We need about a gallon per person per day, so 2 bottles is a day for 1 person. You may get by on somewhat less.
One thing I have done is fill two of them a bit less then full and freeze them. The will help keep my freezer cool when the electricity goes down. Don't freeze all your bottles of water!

Begin by picking up a 1 or 2 pound bag of rice and dried beans. It may not be great just by itself but what I have just mentioned will give you about 3 days for 2 people. If you can afford it, get a can of chicken stock and use it to cook the rice. Someone mentioned adding bullion and that works, but it adds a great deal of sodium.

Can you get your hands on some canning jars? Around my area just about every neighbor has at least one fruit tree and fruit trees do not spread the harvest over several weeks, it seems that 100% of the peaches are ready in one week. We all share with one another. Perhaps you can do the same and can some of that bounty when it all comes in.

Keep reading and every day is a day to do something small to prepare!