What Image Size to Copy Photos to Note 4 and Chromecast Them?

[pwscott]

I am trying to decide at what resolution and size I should export photos for sharing on my Note 4. Liek if I shoot with my D-SLR that is 20 Megapixels, how big should I output the JPEGs from Lightroom? If I decide to share them with a Chromecast or something on a plasma TV I'd like them to look good. Not that worried about space...But it seems some higher res images can;t display in he gallery...? Thoughts?