Welcome from Central Texas.
There is a very good checklist available on the site. (link below) Use it as a
starting point and tailor it to your specific needs. I personally didn't need some of the items listed, and yet also added many things that are not listed.
The Ultimate Overland Checklist
We've camped everywhere from Padre Island to the White Mountains to the moors of Scotland, in everything from a small 2-person ground tent to a 32' travel trailer. Every trip is different, thus every trip's needs are different.
I wouldn't worry too much about upgrading your rig at first. You won't always be going rock crawling just to go camping. Start small with the basics and work up. Once you get a tent, set it up and take it down in your back yard several times. Do this with everything new you get. The more familiar you are doing this now, the easier (and less stressful) it will be on site at 0-dark-30. Last thing you want to do is try and figure out how to operate something for the first time when it's dark and raining.
Get the sleeping gear YOU want. Like a sleeping bag and mat? Fine. Want an air mattress with blankets instead? That's alright, too. You are the one that is going to be using it, so whatever makes for a good nights sleep for you is what you should get.
Get a small propane camp stove, a 5 gallon water container, an insulated cooler, a camp cook kit, and some canned food you can heat up easily like soup or chili.
Now, take all this new gear, pack it in your truck, and head out to a nearby state park for a weekend trip. This will be the first of several trial runs. This will give you an idea of what you do/don't need before you head off on a much longer trip, where you may not be able to just run out and pick up something that you didn't think about or got left behind. It will also help you determine just how much you can carry and the best method of packing it all up. Overlanding/camping is a dynamic process and there really is no "done" list. So, bring a notepad and pencil every time to make notes of things you need to change, add, or remove. Your gear will evolve and adapt to your needs over time and before you know it, you'll have everything you need.
Lastly, get to know your local OB members. They are a great resource!!
Note: a good first aid kit, flashlight and fire extinguisher should be in your rig at all times anyway. Don't skimp on them.