Hrmmmm, I've never owned texas or green terrors...but I do keep plants with various other cichlids such as EBJD, thread fin acaras...I've kept geos and parrots with plants as well, rainbow cichlids, t. ellioti...its possible so long as you know your fish.
Now, given that you are new to plants, this will be intereting. What's your substrate like right now, and what size tank is this? I would suggest to you starting out with something that will be low lighting, I can tell you what that would be like once I know your tank size. Your substrate will help determine what kinds of plants would be best. I think for your sake, things that get strong roots would be wise. I'm thinking swords, lotus plants, and hardy stems like hyrgophilia species and some easier ludwigia...anubias and java fern can be attached to the hardscape, as well as mosses. And of course there are floating plants as well, but you might not bother with those if you are doing low light...maybe in medium though, we'll see.
Post a pic of your tank, and also, I'd avoid natural sunlight as its not consistent and may cause algae. I like to be in control of my lighting.
How big are your cichlids now? I've noticed that cichlids do better with plants when they grow up with them. Worst they do to plants ever is just dig them up, never really destroy them....except for my rainbow cichlids with water sprite and wisteria...for some reason they ate those specifically but it might have been a phase.
Biggest rule with keeping plants and cichlids, don't give up if a plant doesn't work the first time. Eventually they leave the plants alone and get bored of them, I've also noticed that cichlids kept with other fish (such as tetras and other dither type fish that divert attention) tend to ignore plants.
Only time I've had problems due to cichlids was when my rainbow was trying to convince the other rainbow to spawn. He failed and so he stopped digging up my plants in that area, now he's content with it, or has accepted that he isn't getting anywhere with that lady fish