[Build Help] Upgrading ram and video card of an old machine. Basic help needed.

I have this computer. I want to upgrade the ram and video card.

• What type of video card is required and can I get one with a HDMI jack?

• If I go to 4 gigs ram (keeping in mind the aging dual core processor) will I be able to run a 64 bit Ubuntu install that actually takes advantage of it? Would 8 make an difference with this old hardware?

Edit: asked about 8 gigs