OK, I gather you question asks "What's best based on my TV's capability" and not "What's best if I start from scratch."
IMO, the best is a dedicated HTPC (Home Theater PC) as the playback client to ANY TV (doesn't has to be smart since the HTPC *is* the brain) and a NAS. I prefer the HTPC as its user interface is so more flexible, configurable, scalable, much-much-much better in performance (smoother and faster navigation) vs the Smart TV version.
A SmartTV based video playback platform is based on the DLNA model (WIKI for full details). I call it the lazy-man system and it's intended to be a quick way to get things going, and as you will find out, it's kinda limited (unbelievable after you spent what extra dough on that Smart TV right.). For example, my TV's DLNA Interface has NO SEARCH function. What happens when you accumulate hundreds and thousand of videos, how are you going to get to the one quickly?
Anywhoo, enough trashing DLNA. Try it, is already built-in so give it a try, can always upgrade later to a full blown HTPC. What you currently need is a DLNA server, and the quickest way would be via a NAS that has DLNA capability. A Western Digital I hear often. That way you access it via your desktop as desired for maintenance etc.