What is a good native image size to use for a full width (100% of browser) slider?

1920px is the highest you want to go. That is considered the "high-end" for screen resolution sizes, and anything higher will make the browsers act up. As long as you set your slide width to 100% it will adjust to screen sizes of a higher resolution than 1920 without a problem. This will also solve the problem of taking up too much bandwidth and won't affect your load time (which is key for functionality of your site).