Wraps are probably the easiest type of carrier to do DIY. You are right that it is just a long piece of fabric. I am not sure about your size, but the average length that I usually hear moms say is more like 5-6 yards. I think it is always better to have too much fabric that you can later shorten than not enough fabric to do what you want.
Stretchy wraps are great for newborns. They are generally made with a comfortable knit or jersey fabric. The problem with most stretchy wraps, and definatly with the fabric thatyou will find for a DYI is that after a while the fabric will do exactly what it is intended to do and stretch. Once the fabric starts to stretch under the weight of your baby and causing them to sag, it will be much less comfortable for you. Stretchy wraps are easier to learn to use, because the stretchy fabric is more forgiving, but they are also limited in the positions you can do. I only recommned a front carry with a stretchy wrap.
If you wanted to upgrade to a more supportive wrap, you can look at buying osnaburg, or even a cotton gauze. Gauze will be nice and lightweight for the TX summers, but it will not be as supportive and people often complain that it can dig in if it is not wrapped just right. Either way, gauze or osnaburg, it still will not be the same as getting a true woven wrap, but it will be enough for you to see if you are a wrapper and want to invest in a better woven wrap, or if wrapping just is not for you.