I'm a novice at this and just completed my first theater build. With that being said I do think I can give a bit of advise as I used a similar sized room and I like to stretch my dollar as far as it will go. Since I'm not a professional or theater "snob" I think I can also relate to what you will find important and what isn't that critical to the average person. That being said I think the most important advise is what BIGmouthinDC said, if you are going to do it, do it right. If you're going to take shortcuts you will either be unhappy with the results or future potential buyers of your house will be unhappy with your results. I recently purchased my new home and I either wanted things to be done the right way or I wanted them so that they didn't interfere with me using the space in a way I wanted to. If you start building 1/2 complete walls and such you are asking for problems down the road.
First thing I would recommend is that I would place your theater as you have in "option 2" but I would place the play room as in "option 1" much like Tedd has suggested. Do you really want to have friends over to watch a movie or ball game and have kids running through the theater to get to the playroom?
With the size you have dedicated to the theater you have a couple of limitations to both screen size and seating. With seating you will not want to go more than two rows, if you go more with that size room the front row will be the equivalent of sitting in the front row of a movie theater. This is assuming you do a seat riser and I would recommend you go that route for a theater room. The riser itself will need to be 6' to 8' in depth and 8" to 10" in height. It seems cool when you are 6 but who else wants to be 5' from a large screen? You will also be limited to about 3 seats on the front row and 4 seats on the back row (could go more seats on the back if you go with a bar setup but not with recliner type theater seats or a couch).
Your screen size is going to be somewhere between 110" and 140" and this will depend on your ceiling height and also your speaker selection and how much room to the side and bottom of the screen you need to dedicate to speakers. I know someone on an earlier reply mentioned doing speakers behind an acoustically transparent screen but that type of screen is more expensive and will eat up about $600 of your budget compared to $315 with a normal screen (for 120" screen if you shop around). In hindsight I wish I had spent the extra money and gone transparent but my budget was about $7000 which is more than double what you wish to spend. In your case this might make more since though which I will get to in a minute. You can get by cheaper if you purchase screen material off E-Bay and build your own but it will probably not be worth the extra work and lack in fit and finish as compared to buying a complete framed screen off Amazon.
Speakers: Someone earlier recommended against in wall speakers. I used to have the same mind set until I checked out a friend's theater and was satisfied with the sound he got from his (other than they were not properly set up). By the time I did my build, and considered my "limited" space in terms of theater design and I was committed to going in wall. I started out wanting to go cheap but came to the realization that if I was going to cut 7 large holes in my wall I needed to get decent speakers. With that being said either get good in wall speakers or don't do in wall at all. By good I mean you are going to spend at least $200 per speaker, not counting the sub-woofer (I have seen some speakers as low as $85 each that "might" be decent but I have not heard them in person). If you don't want to spend this kind of money I would recommend standard speakers in which case it might make more since to spend a bit more on the acoustically transparent screen to hide your speakers behind. If you wish to message me I will tell you what I recommend to get the best bang for the buck, speakers are subjective and if I list them here it will start a whole new debate.
My personal budget for what you are doing in your budget would be:
$315 for 120" framed screen.
$350 for surround receiver.
$1000 for in wall speakers + sub (special deal I'll tell you about if you send message).
$150 speaker wire.
$40 projector mount
This would be in addition to any construction cost, seating, etc. If you are not picky at all the item you could save on would be the speakers in which case you could go to Wal-Mart and get a receiver + theater system for $300. This would knock $1050 off what I have listed above. This would take away from the "theater" experience but to each their own.