What are the best conditions country can offer for private R&D?

How much working capital do you have? Are you able to establish residency in any country you like? Have you looked into which type of entity you want your business and how to structure it? Can you be the owner of the entity as a non- resident? I worked with companies with my accounting firm in New Zealand. Your question simply raises more questions and your plan sounds not very well thought out yet.

It looks like you’re putting the cart before the horse. You should narrow your focus. AI, Stock Market and Antivirus are very different areas of research. It’s a bit like saying I’m going to open a restaurant that does crepes, tamales, and sushi. The best country is the one you’re in right now. If you’ve got a computer and an internet connection, you can research all of those topics to your heart’s content.