Jmath: Ported subs will be bigger and have more output at their tuning frequency. The smallest ported sub that SVS makes (not including their cylindrical designs) is the PB-1000. It's 15" W x 18.4" H x 18.4" D not counting the grille, and weighs 60 lbs. It's also within your $500 budget.
Matching room size vs. subwoofer size/type is a key element in bass enjoyment. Your room size falls into the medium size volume. If it is open to other rooms, it may fall into the large size volume. For music, the PB-1000 may be enough depending upon how loud you listen to music, what type of music, and what you really expect from a subwoofer. However, we are all different and we all listen at different levels and to different music. Most people here seek reference or near-reference levels and want to feel room pressurization. Most here will also recommend multiple subwoofers. The reason for multiples is solid. It allows for a more even bass response in a wider and deeper area within the room (your seating positions), and all rooms will have peaks and nulls (sometimes severe).
Sound difference. I have found that the comparable subwoofers I have auditioned (all sealed designs) sound similar with most types of music, however, I could easily judge which sub I preferred with certain pieces of music I listen to. Sealed vs Ported would, I assume, sound similar as well, but that doesn't mean you would automatically prefer sealed over ported. You may or may not -- each person is different.
Someone mentioned here (and I'm paraphrasing) that getting a sub isn't a means to an end, it's the beginning of a long journey.