+1 on the carpets being challenging. You will need decent lighting for reds as well. I realized that tall tanks would require stronger lighting so I stuck with 20g long because they are not deep.
I started a planted tank last year with what I thought was decent lighting (inexpensive dual T5 NO). But only a few of the plants actually grew. A few months later I switched to a Finnex FugeRay and growth improved for most of them (some had died out). Next I added DIY CO2 and in the next 6-8 weeks some plants went bananas! Two in particular: Bacopa caroliniana and broadleaf chain sword. For ferts at the time I was using API Leaf Zone, Seachem Flourish Comp and occasionally Excel. Trimming the Bacopa every week or two. I was removing about a dozen chain swords a week. I eventually removed both plants because I got tired of trimming them (they became invasive). As for a carpet, I tried dwarf sag but it grew too tall. Same with the broadleaf chain sword.
Fast forward to this year: Here is a somewhat recent pic showing three carpet plants. From left to right: Downoi, Alternanthera reineckii (AR) mini, and Staurogynes repens
I recently switched to pressurized CO2 (AquaTek Premium) and PPS Pro ferts. I just ordered the Finnex FugeRay Planted + which should arrive today or tomorrow. I'm not getting the growth and color I want out of some newer plants and the planted + should address that.
That being said...DIY CO2 will work, though from what I've read here, it is more effective in tanks 20g or less. I used it for about 8 months and was pleased with the results. Some carbon (CO2, Glut, Excel) is better than nothing. The reason I switched to pressurized was because I started growing some more demanding plants and using stronger lighting.
The lights and plant selection should dictate your need for CO2. Here is a pic of a shrimp tank with the SAME dual T5 NO lights that I removed from my other tank. Plants consist of Crypt undulata, Crypt wendtii, dwarf sag, and a mixture of mosses. The low lighting does not cause over growth and the crypts stay on the smallish side. No ferts or CO2. Occasional root pellets. Very low maintenance. I've trimmed the moss back only once or twice. The older crypt leaves simply rot and dissolve within a few days (no trimming).
Yes, it's good to learn from your mistakes. Sometimes better to learn from other's mistakes. Good luck with this.
BTW - that looks like a val in your tank. A bit too large for that tank. I grew them in a 55g and they would growth 5' plus. Low light stem plants are a good start.