I have a vision of producing future chess stars in a country and I am looking for tips and advice on how to go about it. What would be the best approach or programme to adopt in achieving this dream by working with under 16 players (4 - 16 year olds). I would be interested in areas of study, approach strategies, and any other information that might be vital to chess development on a national scale.
I'm not sure there's one best way. The best way depends on the country: current chess level, number of chess players, the country's economy, etc.
That said, assuming we're talking your country specifically i.e. Botswana, or more generally a developing country where chess isn't very widespread, the first thing I'd look into is the funding provided by FIDE's Planning and Development Comission (PDC). As of 2019 they offer up to 20,000 USD that can be used for purchasing chess equipment, organizing tournaments, etc.
In fact, as you can see on PDC's website, Botswana's funding request for 2019 has been approved. So you should check with your national federation and see how they plan to use the money.
Now if we're talking about a hypothetical situation where you can decide how the money would be used (e.g. for 2020), I'd suggest:
allocate a small part (say 20%) of the funding to improve the situation for existing players (including adults): purchase chess sets, organize free or cheap tournaments, organizer an arbiter seminar, organize classes for intermediate/advanced players, or even provide coaching to players likely to play in the Olympiad. Note I'm not suggesting you do all of these, as $4000 isn't that much, just what you need the most.
allocate the bulk of it (say 80%) to the long term vision: for example, train chess instructors -- think Developmental Instructors in FIDE parlance, that is, people who can teach the rules and the basic of chess to beginners, not FIDE Senior Trainers -- and then provide cheap or free classes to children on weekends or after school.
Ideally you would institute chess classes in schools across the country (like in Armenia), but of course that's very hard to pull off. Still, you can use the Armenian case as an example. You want to convince parents and school teachers that spending time on chess is beneficial for kids, that it's associated with good outcomes. Example article.
You want to focus on elementary school children. It may sound harsh, but if your goal is to produce masters, starting at high school is a bit late.