Those are nice boxes, but not really mobile. Most veggies can be grown in containers with little effort but if your going to be moving I would recommend something with a bottom.
Larger porch pots work well, start small so you don't get overwhelmed. Also, look into "companion planting". This will help you maximize your output with your resources.
Good luck

Pot gardening is a great place to start, especially if you move often. You cannot practically grow all vegetables in pots, but you can grow a lot: tomatoes, peppers, eggplants, lettuce, onions, garlic, cucumbers, some squash, bush beans, broccoli, carrots, and on and on.

Think BIG pots: at least 15 inches in diameter. The bigger, the better. I would recommend the book "The Bountiful Container". It is the best that I have read on growing vegetables in containers.

Agree that the raised beds on the link you provided are just that - raised beds, not containers, and would not be moveable even if they had a bottom in them.

But containers can be used as others have said and the Container Gardening forum here is full of info on the sizes to use for various vegetables, the proper soil mixes to use, and the vegetable varieties well suited for growing in containers.

Since you will be moving them you'll need to balance the size of the container used with the ability to actually lift and move it. In most cases the bigger the container the better the results but the really ideal sized pots 10-15 gallon size would be very difficult to move.

Meanwhile determine which Indiana gardening zone you are in or will be in after moving - there are three of them with very different planting times - and you can use the winter to research the proper planting times for that zone.

Indiana Gardening zones

Also explore all the gardening resources and info available from your state and country extension offices. Just Google 'Indiana State Extension services'. It is based at Purdue Univ.

Dave

Here is a link that might be useful: Container gardening forum

Welcome! You should definitely try growing a garden in pots of some sort.

I would encourage you to stay away from tomatoes on your first year since you might be moving. Growing them in pots is difficult (I have not had much success) unless the pots are pretty large (hard to move!). You might try a cherry tomato though. They are more forgiving in small pots. They do need some kind of tall stake or trellis.

Lettuce, spinach, carrots should do great. Strawberries (if you have the climate). Herbs.

There is also a forum dedicated to container gardening. You may want to read stuff over there. Check out the FAQ. I'll add a link, below.

--McKenzie

Here is a link that might be useful: Container Gardening Forum

My advice is :
Do it small scale and learn from your experience. Then the following season you can decide better how much you can handle.

What about a community plot or find an empty lot that you could use, near your current place as well as where you might move to?