The technology has greatly improved from the time it was commonly referred to as "screen scraping". Currently more commonly referred to as web scraping, or data scraping, is mostly done using automated headless browsers, which are able to return cookies, execute JavaScript, etc., making it much easier from a technical point of view. If the site you are scraping doesn't defend itself against scraping (but simply hasn't bothered to expose the data in API form), you should be able use a cloud scraping service like those offered by AWS and Google, for example.
The problem usually lies in the fact that you are probably doing something very much against the website owner's interests, and probably violating their terms of use, exposing yourself to lawsuits, etc.
In the examples you provide (Best Buy, Amazon), the content is very much central to their value proposition to customers, and poses a significant competitive advantage (people prefer to shop on Amazon because they trust the reviews there, for some reason). They would have to be convinced that they will gain directly from your use of the content, and that you will safe guard this content against their competitors as diligently as they do themselves (of which it would be tough for a startup to convince them).
If you do not have their permission, you will probably find that they spend vast resources to foil scraping attempts, e.g. by blocking or serving fake responses to requests they are able to identify as scraping attempts.