The best app I have found is Mx Player. VLC is also very good.
You need to connect your Galaxy to you PC and, after the drivers have installed, it will show as another device in "My Computer". Open it and navigate to the Movies folder. Just drag a movie into the folder ( you may need to convert it to MP4 standard. Handbrake is a good tool to do so.) Samsung also provides their own PC tool called "Kies" which you can also use to transfer files, backup your phone etc..
Disconnect the phone, tap the Mx Player to open it and your movie will show as ready to play on your phone.
Chromecast is just one of the methods of playing your movie on your TV. There are many others which a Google search will reveal.