First hello and welcome to TPT!
Great job on researching a lot before buying anything, it is critical you know why are you buying something, how it works, and why it is better than option B or C.
Now some thoughts:
1. The ADA Mini M is a great choice! It is small and has nice dimensions and is easy to scape with and water changes will be easy (you will be doing ALOT the first month). I wish I had started with the Mini M, it is perfect for beginners and not overwhelming. While still giving you plenty of choices.
(My favorite best value ADA tanks: Mini M, 60-P, 75-P and the 120-P. )
2. ADA Powder Amazonia 3L is a good choice as well. Adding the Power Sand Special S 2L underneath will give you more depth and bonus nutrients/bacteria etc.
3. LED are awesome lighting systems indeed. DIY is fine, have you looked at the AQUASKY for the Mini M though? I have the 60-P one and the shimmer/brightness is unreal. It will also match the Mini M nicely and is plug and play with the stand included.
4. I don't think the ADA kit is cost wise as it is about $15 a month on CO2 to run.
I would recommend a GLA Prebuilt Atomic Regulator for a paintball tank or 5lb tank.
For Nano tanks, a lot in the US use 20oz or 24 oz paintball CO2 tanks. They are inexpensive to acquire and refill.
5. Aquascaping materials are your choice.
Some other notes:
- I would recommend a pad or ADA garden mat under the tank.
- I would also highly recommenced investing in a pair of quality pinsettes (the longer the better). I planted by hand once and it was extremely difficult and I do not recommend this for a beginner at all; esp if you are planting foreground plants like you want.
- Filtration I don't see mentioned. Short and sweet an Eheim 2211 and ADA Nano Lily Pipes is what I recommend.