Lots of questions : I will try too give you some good answers.
First order of importance some considerations then I will answer your questions:
The most important speakers are the fronts. There are very good book shelf speakers; their only downside is because of their size they can't support good bass sounds. However a good subwoofer solves that problem.
If the HT is going to be used for movies/TVs/DVDs it is important that the center speaker matches the fronts; this means not only the same manufacturer but same series/size. The reason for this is it maintains front timbre -seamless front sound. The center speaker provides most of the dialog.
Subwoofer is next in importance because it provides the bass and lower frequency sounds. It can be a different manufacturer and can be placed various places. It is best to "walk-the-sub" and place in allowable spots to see which sounds best.
The rears and other surrounds are least important. They are used for enhancement and can be smaller and/or a different manufacturer. I would add them later but prewire now.
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Now for your questions: ( I think I already answered some

)
Ok, got it. Speakers first.
Do speakers usually have a range at the wattage that's best for them?
Yes , But I wouldn't worry about it because you are usaully well below the max and can handle the power supplied bymost receivers. The only thing to watch for, especailly for bookshelf, is that you are not approaching the maximum limits. For example if a speaker is reated having a maximum of 100 watts, It would not be good to drive it with a receiver that puts out 100 or 120 watts per channel if you plan to drive it close to maximum volme.
Since the room is open in the back I plan on spending less on the 2 back speakers, is this advisable?
Yes , spend less the surround speakers are the least important speakers.
If fact, i would add them later. Or a pair of the Cambridge Audio S30s ( mentioned below) woiuld work very well
Would it be a good idea to build an enclosure with a front facing sub and put it in the bottom of the right cabinet? I or my friend's dad can do the carpentry work for that if it would be best.
Unless you just want to hide the sub, I would not plan on doing that. It might actually interfer with the sub sound. The sub can usually be placed in the back of the room or somewhere else where it looks asthestic and is not obvious. Also good subs are pretty big and the cabinet to enclose them would be even bigger.
Can I get them a decent sound out of bookshelf speakers, cause my mother will not stand for getting floor speakers?
Absolutely. here are some recommendations.
Cambridge Audio S-30. They are small but provide excellent sound. The can be purchased for as little as $199 per pair.
http://www.digitalcraze.com/Details.asp?Source=Froogle&ProductID=3969
An even better bookshelf speaker is the Mordaunt Short Mezzo 2 Bookshelf speakers for $794 per pair.
http://www.wildwestelectronics.net/mezzo-2-bookshelf-speaker.html
Do R/C/L speakers have to match from the same line? Well I mean I'm sure it will physically function but say one company has a better sounding center than another and you have (for example) a polk center and klipsch L & R. Would it still sound good or would getting all 3 from the same line be the best solution over others.
Yes, the R/C/L speakers should match to maintain timbre -seamless front sound.
And yes, the absolute best match is 3 identical speakers. If you get the Cambridge Audio S30s then get a second pair and use one for the center or get a matching S50 (which is sometimes hard to find in USA).
The matching center speaker for the Mordaunt Short Mezzo 2 is the Mordaunt Short Mezzo 5 Center Channel speaker for $595
http://www.wildwestelectronics.net/mezzo-5-center-channel.html
What size of a sub do you think would be best for that size room? And what about placement, would putting in that bottom right cabinet be less than ideal?
I would get a SVS or Hsu subwoofer. The room looks to be large,so you need a fairly large sub. Rahter than getting a cheap sub,which will sound cheap, it is better to save up an get a good sub.
The SVS PB12-NSD cost$ $569 and would provide good low frequency bass sounds.
http://www.svsound.com/products-sub-box-pb12nsd.cfm
The Hsu VTF-3 MK3 subwoofer costs $699-$799
http://www.hsuresearch.com/products/vtf-3-mk3.html
Anyway, just one last question. Could you recommend some quality speaker and sub manufacturers at which to look? Of course I would never buy speakers or let my parents buy them without listening to them in person.
Is always best to audition speakers if you can, but Cambridge Audio, Mordaunt Short, SVS and Hsu are excellent brands you can buy with confidence without auditioning.
And finally an answer to you original question. The AVR receiver. The offer by Audioholics Online is an excellent receiver which will meet your needs, the Yamaha RX-V365 Surround Receiver for $229.95
http://store.audioholics.com/product/2360/66343/yamaha-rx-v365-surround-receiver
Good Luck!
NJ
P.S. - The room looks great
Thanks again![/QUOTE]