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Since media formats are cyclically outdone by newer technologies, your best bet is to invest some bandwidth into acquiring digital copies of your films. For portability and cost efficiency, I think that's the best way to approach building a collection.
DVD's and Blu-Ray's are great, but you're going to have to re-buy your entire collection again in the not-so-distant future. You may think, "Oh, I'll hold on to a DVD/BR player for the next fifteen years." Not only is that easier said than done, but by that time, higher resolution televisions and media formats will exist, and it will be difficult for you and your eyes to "just deal with it," so to speak.
That said, physical copies which are taken care of have a much greater shot at longevity. Unlike an external hard drive, a DVD won't randomly malfunction and clear itself of all the information it holds.