Tetra are probably the most wildly varied fish in the world but there are some very very predictable things about them.
They're very sensitive to ammonia and nitrite.
They're good tankmates.
They'll eat left-over betta food.
They have some vivid colors that vary intensity depending on water quality.
My girl tank has bloodfins, my boy tank has tons of the striped neon kinds and sherbert the half-moon has pristella and gold pristella.
Primarily the red coloration on the fish is what you watch. Intense bright is happy good tank, dim bright is ok tank, fading is either tank getting bad or the tetra is having issues. Remember that most tetra get BIIIG, you're buying fry from the store, not full growns.
I can, at a glance at my tetra, check to see if anything is out of kilter in my tank LONG before my Betta start showing an issue. I've even had a sudden "drastic" change in the five kill three pristella whilst Sherbert swam back and forth in a panic at me because something was wrong with his posse. Sherbert was fine and wasn't showing any signs of problems!
Remember that you really can't just buy "A" tetra. They all come in different preferred minimum groups. Bloodfin need a partner, stellas need three friends and many of the small stripe types need six, eight or more in their shoal. Don't get neon/glow light of any kind with less than a ten gallon even if you plan to later move them, they shoal and that is a large formation that needs space.
So here's me, talking about tetra on the Betta forums, such a troll!