Graphics design question...

So, I am a full time business student and I recently sought (and technically am still seeking) a part time job. So I talk to some people and I say ideally I would like a web design position, part time for 10-15 hours per week(I have lots of experience, a decent web portfolio, and solid knowledge of html, css, php, mysql, and a few other tidbits of languages and know how to fit them together to develop things like a CMS and database based apps). So, someone says yeah I know a guy that needs graphic designer, do you know photoshop. I do webdesign, so I know my way around photoshop, and for that matter Flash, and Fireworks too.

So anyway, I talk to a possible employer and he asks for samples of my work. He knows full well i originally asked about a web design position and it was upon a mutual friends introduction and recommendation that I am now talking to him about a graphic design position. I could go on and on all day about how web designers and graphic designers are really two different entities (well often the same person) that are after two different things. Web designers optimize images for size (small), type (we love jpegs), and 9 times out of 10 would much rather use css to say change a background color, never mind resolution limitations. Conversely graphic designers (artists) want everything perfect, highest resolutions possible, have great depth of color, ect. (well maybe not that extreme, but you get my point)

So here's the question (well questions...), A) What work or parts of my work should I include in my portfolio to submit (or should I just show the entire website?)? B) Should I be working on a few pieces that better show my graphic design talents and if so, any suggestions?

Thank you for your time.