I echo what a lot have said, if your situation allows, start growing your own fruit and vegetables. If not then start with the simple things, the staples that you use every day. Flour, oil, protein foods, vegetables.
A good store of herbs amd spices can make a very boring diet edible.
USU probably have the best resource for online for preppers. I follow a lot of their advice and it has made a huge difference to my food storage programme. I only wish I'd found the resource years ago.
http://extension.usu.edu/homeandfamily
This is a link to their food storage guide PDF. I'd say it's probably the best advice out there.
https://extension.usu.edu/foodstorage/htm/book
I don't know what kind of climate you live in, but I would look on utube and find some videos on home dehydrating you could probably use air drying, If not the best bit of kit you could probably start off with is a simple Nesco dehydrator. There are literally hundreds of videos about dehydrating and if you are unable to access a decent farmers market, I have a lot of frozen veg from the store dehydrated and stored in canning jars.
I don't think there is anything wrong with the buckets, but you are limiting your diet both in flavour and texture.
Finlly and to me this is this is the most imprtant skill you can have; if you can't already, learn to cook from scratch. If you have that skill, you can make a meal with anything.
Good luck with your endevours.