Dont really plan on playing games on it as I have a dedicated gaming PC (apart from League of Legends), but it would be used for media consumption (plugged to an HD TV), programming and net browsing...
I wouldn't dismiss the benefits of a discrete GPU - - any modern laptop worth it's salt needs to have one these days even if you don't see the need for one right now, think about what you might want to use the laptop for in the future.
Graphics editing also benefits from a high-performance GPU, not just games.
The Intel HD 620 will not have any issues outputting video to a HDTV. It can do 4k video at 60 FPS. However, I believe it is only possible if the laptop and HDTV have HDMI 2.0 and you are using a HDMI 2.0 compliant cable. Otherwise it defaults to 4k at 30 FPS.
I have basicly decided on a better processor. The model that fits my budget is the Lenovo Ideapad 320 with the i5 7200U, but im not sure if I should get it couse reviewers say it has a bad screen. Would an Hp 250 G6 with an I3 6006U and a Radeon R520 card be better (looking at the screen)?