Honestly you probably want to do both. There's going to be movies you'd never thought to watch or ever hear of because they either didn't get much attention.

Mainstream, or popular movies will usually be streaming somewhere - but more art house or rare films may never hit streaming. If they do it'll be on a niche service more than likely.

You could invest in your own personal streaming system, i.e. build a server and upload your collection. But if you're not looking to invest into this...

I recommend buying any film you plan on watching more than once. If you're finding yourself watching a specific set of films constantly buy these. In the end you support everyone that made the film.