Before you start ordering equipment, you might want to step back and think about the logistics of getting everything in your room first. 13' x 13' is tiny to begin with. You probably also have a door, a closet, and at least one window that will play into locating your equipment. Then there is furniture... what kind of seating? What kind of display, and is there a stand or equipment shelf/cabinet/rack associated? Other furniture like coffee table and/or end tables?
In a room like this, sadly, these type of logistical challenges usually need to take precedence over placement for absolute sound quality. A sketch/picture of the room and your proposed layout along with everything else that will be in the room would help a lot in anyone making recommendations. Again, it's unfortunate, but the "where" might need to be decided before the "what" with this type of room.
I'm not coming at this to be a complete naysayer or without having had been in a similar spot before... actually, this is a lesson I've learned by not having the flexibility to chose equipment like you do now. My first home after getting married had my equipment stuck in a similarly sized spare bedroom. All my equipment was stuff I already owned, so I shoe-horned it into the tiny space (large tower speakers, 92" projection screen, equipment stand with center and electronics under the screen, 5 cuft DIY sub, etc)... after all my gear was in, I only had room for 2 folding camping chairs for seating with the sub doing double-duty as end-table between the two chairs and projector stand... and this was even after picking up a pair of tiny bipole on-wall surrounds to free up some floor space around the seating.
I lived with the setup for about 9 months knowing it would be temporary, but had I been buying equipment strategically for the space and for more long-term use I would have done things much differently. First, a few questions...
1.) What type of display (LCD/Plasma, DLP RP, Front Projection)? How will it be mounted (on-wall, stand, cabinet)?
2.) What type of seating?
3.) What immovable room impediments exist (entry door, closet(s), window(s), etc)? A sketch or picture would help.
4.) Do you own the home? Can you wall-mount the display, use in-wall speakers, etc? If you don't and you can't, how long will you be in the current home?
I was about to let you know what I would do making some assumptions on the above questions, but honestly, the display/seating/room is too big of an impact on the equation to even make wild-guess recommendations.