Are there issues with embedding large video files?

I want to make a blog that will be very visual, and focus on lots of videos and images. I am noticing that most of the themes that I am finding are not set up to enable very large videos from being embedded on a post. Most have small videos. I will likely be embedding videos from either Youtube or Vimeo. I would like the blog to be viewed nicely on laptops, computers, phones and tablets.

1. Are there any issues with embedding videos that take up almost the full width of a page?
2. Anyone have any suggestions for the largest size I should consider embedding these videos based on current standards?

Thanks!