With the Arc/Era/Sub combination for the media room that will give you an Atmos-capable system and is then the most speakers you can have in a Sonos system - except another Sub should you feel the system needs it. 
 

In the main open area, if you don’t have a tv you don’t need the Arc. Instead consider Fives or Eras. If it’s a place you want to listen to music, set up a stereo pair in front of your main listening position. If you want a room-filled sound, consider another pair of the same Era-or-Fives and group them together to play in sync. And then group the media room too for sync’d music throughout the space.
 

Note though that because of the way Sonos works, there will be a 70msec delay to audio from a tv signal to rooms other than the media room speakers. if you’re in the open space and can’t see the tv that’s fine though there will be a position between the two rooms where you can hear both lots of speakers equally and in that location it will sound like an echo. (Don’t stand there and all will be fine!) I often listen to tv programs in the kitchen if I’m in and out whilst cooking, and there’s a spot in the doorway to the kitchen where I get the effect - but I don’t stand there…

Thank you for your reply.

I understood your suggestion for media room. Just buy one ultimate system and install.

open area I would like music all over.  So for that you said no arc but put 2 era 300. Would they be enough for the open area. 
 

not sure I understood the Tv signal part. When I will play music I would like the same music to playin media room and the open area and it might be played through media room TV or via iPhone. Would that not be possible?

are you saying that if I played music via TV then there is 70 msecd lapse but if I played via iPhone then it will not be a problem.

To achieve synchronous multiroom music, Sonos buffers a bit of the data stream before playing. With no visual cues it doesn’t matter, but with lips on the video moving out-of-time with the audio it can be quite off-putting. Audio to home cinema systems has a minimal delay so this isn’t an issue, but when grouping other rooms, the delay has to be there when sending the audio to those other rooms - but only to those rooms. Sound in the home theatre system is not affected. 
For the room-filled sound requirement, try with 2 Era 300’s. If it’s not enough, add 2 more. You can set them up as 4 rooms, each with one Era in it, or 2 rooms, each with a stereo pair, and then group to get them all playing together. The reconfigurability of Sonos devices means you can play with combinations and see (hear) what you like best. 

Thank you again for your response. Hmm so if I set up all era’s as separate rooms wouldn’t that be bigger issue with playing synchronous music. What am I missing here?

I understood the rest. Thank you again 

Streamed music across multiple speakers/rooms will play in sync. The only time a delay will exist is if the source is from tv, as I (hope I) explained above.
 

Grouping means you select the speakers that you want in that group, and a source (Amazon music, something on your iPhone via Airplay, etc).  The selected music will play to all speakers in the group - even to your home cinema speakers. 

The act of grouping speakers set the Sonos magic to work. AIUI, a speaker is set as “master”; the music source goes to it; it sends the same music to the other speakers in the group, together with synchronisation signals. If a speaker misses data it notifies the master and receives the data again. Provided that your network is robust, a sync’d group should be able to play pretty much indefinitely. 

Thank you so much. It all makes sense now. Very new to this so it took some time for me to understand you have been extremely helpful. 

My shopping list would be 1 arc, 4 Era 300 and 1 sub (3rd gen) for the whole area and then go from there. 

I am going to ask the contractor to put outlets on all corners of the ceiling so if we need to move the speakers around we can without hassle.

Enjoy! Maybe too, report back with how you decide to set them up: others may be interested. 

Absolutely!! It might be few months as dependent on contractor to finish our basement :)