So I found the digital camera I want to buy, but I'm not sure which SDHC card to buy.
Do I have to buy an SDHC card from the same company as the camera manufacturer?
Do I need to buy anything to get the photos, and video off the card, and onto my PC?
If the camera says it can go up to 4gb, can I go up to 8, Will it hurt it?

Just wondering before I shell out $20 and find out I can't even get the images off the card, or the card is incompatible with the camera.

You will need a card reader that supports SDHC. The 8G card should be usuable. It probably only lists 4G because the literatire was written before 8G SDHC cards were released.

Any SDHC card will work.