Welcome to the hobby. As for your questions...
Your tank is 23 liters (6 gallons). Normally a rough estimate of how many fish you can have is 1 inch of fish per 6 gallons. Other things factor into this as some fish are messy or have a larger bioload than others. The fish you suggested are good beginner fish and like to be kept in schools of at least 5. I would stick to just the neon tetras for now, and maybe get your school up to a total of 6. Having both of those schools in a tank your size would be overcrowded and possibly make it hard to keep everyone alive and healthy.
As for the shrimp, the only 100% shrimp safe fish is the otocinclus, any other fish may try to eat or harass the shrimp. They can be kept together but sometimes it doesn't go well. Cherry shrimp are normally very easy to breed but any babies you have will be eaten by the tetras for sure. The adults may survive and do ok. The more plants the better so they have more areas to hide. If you wanted to have shrimp, I would suggest doing a shrimp only tank, as that would be very doable in a tank your size and you could have a breeding colony of up to around 50 or more shrimp in that size tank.
As for plants, the ones you listed are good starter plants. Plants in general lead to healthier tank and help oxygenate and clean the water a bit. Other good starter plants are hornwort, anacharis, and frogbit. I keep all 3 of those and they are easy to keep even with my black thumb, haha.
As for substrate, a darker substrate will help bring out the colors of the tetras and/or the shrimp. You could get some black sand or even small sized gravel. Make sure its aquarium safe stuff though and rinsed well.
As for chemicals, wait and see how the plants are doing, generally they will get most of what they need from fish waste. Let us know how your growth or condition of plants are doing, and other can help suggest fertilizers if needed. Less is more generally in this hobby, especially when you are starting off. Don't want to have to make some chemical soup to complicate things. If you can keep it simple that will help.
As for lighting, I'm not sure about what kind of light you have. The main thing you are looking for in lighting is for the color range to be about 6500k. This is generally preferred by most plants. If your tank came with a light fixture it is probably bright enough to support most starter plants. But if its not the right color range (6500k, or close) it won't support healthy plants. If it's not, you should probably be able to replace just the bulb to get a better more plant friendly color range.
You have the right idea to start with of adding things slowly. Patience is your best friend in fish keeping, and will lead to happier and healthy fish/shrimp. Reading and research will also be your new best friend. There is a lot of info here on the forums to help you out. Use the search function to help find out anything you may be wondering. And of course post any questions you need to elaborate on. I hope this helps and let us know if you need any more help, good luck. Welcome to the plantedtank.