Home network setup - including media

Question

Hello!  Here is my family's current set up:
Apple TV 3rd Gen (qty 2)
iPhone 6 (qty 2)
MacBook Air (qty 2)
iPad Air
iPad 1st Gen
Mac Mini (2.6ghz i7, 8GB RAM, 1TB HD)
2TB Airport Time Capsule
My ultimate goal is to fully cut the cable TV cord in the next month or two and work exclusively through Apple TV.  We basically watch several shows; Modern Family, The Middle, Walking Dead, Game of Thrones, and football.  We will of course browse through other channels if bored, but usually if those aren't on we'll just hop over to Netflix.  Between a digital antenna to get ABC and the other network channels and probably just getting a season subscription for Walking Dead and GoT, we should be all set with the other options available on Apple TV (possibly HULU Plus, haven't decided).  My wife's only concern is we will no longer have DVR's, which is a valid concern so I'm still on the fence with that.  I'd hate to get TiVO or something like it for just the network stations we'll bring in with the digital antenna, but I believe HULU Plus has Modern Family and The Middle so I may just get that to do away with any concern.  Basically any shows or movies we watch are on the TV's throughout the house, we very rarely watch it on our laptops or devices.  Only exception is our son who "owns" (ha) the old 1st Gen iPad.  He likes to watch youtube videos on it before bed, but I'm in the process of teaching him how to see his Toy Story and Polar Express movies in the Videos section (through home sharing).  He's 3, so it's taking a while haha.
Anyway, that covering the TV portion of things, I'm left with my iTunes library.  Right now I keep the files and all physical downloads (music and movies) on the Mac Mini, and then it is accessed through Home Sharing by the Apple TV's (and devices if we choose).  I copied my entire DVD collection to iTunes so essentially anything entertainment wise in my house is digital....no DVDs, CDs, etc.
Here's my question I guess....what is your recommendation for how I should set everything up based on what you've seen above?  Below are a couple preferences/concerns I have:
Right now my Mac Mini basically acts as the "server."  It is hooked up to the TV in our living room right now.  I hardly ever use it as a "computer" since we both have our Macbook Air's, but I do use it from time to time if I need to copy a DVD or CD over to iTunes.  Otherwise, it's basically the "server".  I have read several things that talked about using the Time Capsule as a shared drive that would allow you to access it from any location as long as you're connected to internet (I set it up that way and tested it, and it does work).  Should I possibly move my entire iTunes library (music, movies, etc) onto the Time Capsule that way, just in case, I could access all our movies from any location (I know I can already with the music through iTunes match, but that doesn't work for movies).  It's really not a HUGE concern for me right now, but it would just be nice to have.  How would that affect my home sharing setup though?  Would all my devices (including Apple TV's) be able to access the music and movies through the Time Capsule?  Also, would it be slower streaming from the TC rather than the Mac Mini?
This may be off topic, but if I continue to use the Mac Mini as my "server", would I benefit from upgrading the RAM from 8GB to 16GB?  Not sure that affect much, but just a thought.
Right now I don't do the constant time machine backup to the Time Capsule.  I do it about once a month manually.  I guess subconsciously I'm just trying to keep some space free on it in case I want to use it as a shared drive.
Like I said, I have no problem keeping everything on the Mac Mini and using it as the "server", I just want to confirm I'm doing things the most efficient way possible with the set up I have above.
If anyone has any recommendations about the best way I should set everything up (I'm also not against buying anything additional that might make it a more efficient set up) please feel free to comment.  Basically I just want a seamless Apple household where all I have to do is "think it" and then it happens.  Haha.  Thanks in advance for your comments!

Answer 1

Thank you lordstag!! worked perfectly
Linksys
Setup > Basic Setup >
Local IP Address
Before: 192.168.1.1
After: 192.168.0.100
DHCP Server: Disable
Connected network cable from Motorola LAN port 4 ---> Linksys LAN port 1, left the Internet port on the Linksys empty
Motorola
Basic > DHCP >
DHCP Server: Yes
Starting Local Address: 192.168.0.100
Renewed the IP's of the clients
'ipconfig /release' to let go of the address.
'ipconfig /renew' to obtain a new IP address
This is how my network now looks and works
One last question, could this have been done using the Internet port on the Linksys Router?
I appreciate all the help, Thanks again !