If you want to use links for video playback -I would consider Livid or Gumlet. Livid is made by the people behind StreamYard, and it just feels very smooth and polished, much like Vimeo.Both offer free plan but with the branding.
If you don’t mind the pop-ups and recommendations at the end, you can go with YouTube links.
I use my web hosting provider’s server and uploading the videos directly there.