Yes, I know that you were trying to clarify, whereas I was going for simplicity, because the question I posed to R_Wat was the important part of my post. He has replied above, so I’ll see if I can help a guy with his described equipment (cpt, pitch in if you want to.).
Selecting video files from a computer to play works OK if you do not have a lot of them, A My Cloud can store a lot more, and you can also easily stream them to play on a phone or tablet. Since you want justification of using a My Cloud, this is one: it can store a lot more data than most computers (that also must be turned on), plus, if the My Cloud is on and on the home network, it is a lot easier and simpler to play videos from it. You have a lot of space on it for storage, especially if you are just getting started collecting video files. So, start off with a basic My Cloud NAS and select the disk size model you will require.
I am going to presume you have already been streaming movies from your computer to your Chromecast, and you know how well it works on your network. Basically, you need a fast router with fast Wi-Fi.
This is a good time to mention there are now two models of Chromecast (gen1) and Chromecast 2 (or gen2) Google still calls the newest one Chromecast. and it is the round shaped one. The big difference is faster processor and better Wi-Fi ,because it is dual-band and uses either 2.4 or 5G bands. Since I have had the first gen Chromecast, this past month I purchased the newest one for the better Wi-Fi speed and processor, since I do all video streaming on the 5G band.
At the price of a Chromecast it makes $ense to upgrade if one uses their Chromecast often.
OK, since the iPhone and app used to select video to play/cast is what determines what video format will play, they can play/mp4/m4v files and Chromecast can display mp4/m4v files on TV, but other formats are harder to cast if app cannot play video format natively on iPhone. Example is MKV; I really have not found an iPhone app that can do it, but I have not looked hard for one either. You also need an app that has the capability to cast to Chromecast; not all apps can. My preferred iOS app for selecting my video to play/cast to Chromecast is called File Browser; It costs a few bucks, but I think it is worth it.
As I previously said, if I watch MKV files they are ones I made from my ISO files, and they are fairly complex videos that requires them to be played by my WDTV. Watching my MKV files on our 54" TV is like watching the high quality DVD they came from .
So, give it a go, and if the limitations of an iPhone and a Chromecast limit what you can do, it could be time to step up to a more robust and versatile media player like a WDTV, but for now just enjoy what you can watch.