USB-C to HDMI adapter or cable? Asking for recommendations

Hello there, some context:

I ordered a Lenovo y700 for gaming and work. I want to be able to play on my tv and to show slides and media at school too (I'm a teacher). I can't stream or broadcast to the tv (not sure what's the right term) I need to connect by cable.

I don't know a lot about refresh rates and screen resolutions but I'm looking for the best bang for the buck kind of thing. I already have some HDMI to HDMI cables.

Is there any difference between using an adapter or a cable directly?

What cable or adapter do you recommend?