I currently have a HP omen 870-216na with a nvidia gtx 1060 3G and was thinking about upgrading to a 1070 or a 1060 6G, I've done some research and heard that with a prebuilt system the founders edition card is better due to it being a blower style card and the compactness of the case with little vents, is this something I need to take into account? And how much will I have to upgrade my power supply currently at 300 watts?
Yes, this is definitely something to keep in mind as cooling is at a premium in pre-built systems.
If you go to a 1060 6gb, your Power should be fine as long as it has the appropriate connections. If you go to a 1070, you might want to bump the Power to 350 - 400 watts.