At my school we have some masters students studying AI, and they do so using the Unreal engine. They pair up with an art student who makes some 3D models (they certainly don't have to be fancy) and then they work their AI magic in UnrealScript and the Unreal editor, and end up with something functional which can be studied and played with. This is the end goal of AI, after all: an actual game or prototype which demonstrates the AI concepts. Because anything less is just a concept, not a demonstration.
I would imagine you could substitute any engine for Unreal; Unity of course is very popular, and Valve's Source engine is also doing some great AI things. I think the end result is that you need to use all the middleware you can, so that you can get past the foundation and quickly get to actually testing AI concepts.
Many of your questions are very much case-by-case basis. You may want multiple examples of one AI concept each, or you may want one big AI sandbox world with all sorts of AIs running around interacting. It really depends on what exactly you're doing or showing.
Also as a portfolio piece ideally there would be an executable, and videos which should show off whatever is trying to be shown off within only a few minutes.
This isn't a question, so: yes! Also I'd recommend getting a personal website so that you can hopefully direct them to it, or even show it to them in an interview if there is a computer in the room. Make sure the website is as standard as possible; use HTML5 video and Flash (whichever one the browser is compatible with), and have screenshots in case the computer is so locked down that none of these are available. Also if you have a portable video-playing device (iPod, phone, etc.) load up videos of your portfolio and bring that! There might be nothing more impressive in an interview without a computer, than pulling out your insert device here and actually showing the interviewer your work.
Also, one final note: there is a big difference between pretty and polished. It doesn't have to have stellar graphics; but the graphics that are there should at least look finished, not placeholders, no glitches or bugs, etc. Just because it doesn't need to be fine art, doesn't mean it shouldn't look like a finished prototype ready to present.