I might be able to help you out with this as i am an owner of the One mini also
What i have personally done is created a folder on my device storage and named it 'Movies' and i place and videos etc into here. To do this just plug you phone into your pc, let the drivers install, close down htc sync if it starts up as no need to use it for this. You should then get a 'Autoplay' box appear on your computer screen. Click on 'open device to view files' then it will show you the remaining storage you have left, double click on the storage and then anywhere on there right click with your mouse and select 'new folder'. You will then have the option to rename it. Once done you can just 'drag and drop' your files from your computer to your phone.
With regards to playing the movies, i think the One mini plays most file types and by having created the folder you should find that the files should show up in the 'Gallery' application. You then have the option to play them from here. There is a built in player on the device there is no option or app shortcut for the video player. The only time i have seen an option to select the 'video player' is when you have another 3rd party player installed from the play store and then sometimes it will ask which player you wish to use. There are several good ones on the play store and as i can see you have already found one of them in VLC which is very good. Another one i would recommend (i personally use) is 'Dicepalyer'. Lots og great options to vary the speed so it syncs with the sound correctly, also the ability to increase volume upto 400% so great if your file is very quite and it plays blue ray rips so worth having a look at.
Hope this helps
Glad to see someone else with the phone and is enjoying it...was starting to think i was the only person who owned one