Network Infrastruture Upgrade

Question

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Dear Senior Fellows
Good Morning
I am system side person but I have an experience in networks too, now I have an opportunity to handle a large network from scratch. This is educational institute and previous network person just leave the job and I join ,I surveyed the hole setup and found lots of issues ,I will discuss my finding and suggested solution please help me in this regard ,It is great honor for me
Current Setup Findings
Main Site Nodes
Department-1=40
Department-2=100
Department-3=70
Department-4=120
Department-5=50
Department-6=60
Department-7=200
Department-8=50
Department-9=60
Department-10=50
Total=800
Remote Site-1 Nodes
Department-1=30
Department-2=70
Total=100
Remote Site-2 Nodes
Department-1=40
Department-2=30
Total=70
Remote Site-3 Nodes
Department-1=50
Department-2=30
Total=80
Grand Total=1050 Nodes
Now it’s a picture of my Computer /nodes ,All three sites are connect with 2 MB link ,All major departments had Cisco 2900 Switch for connectivity ,Further some departments had their own like allied telyson and D-Link for further segregation, In Server Room we Had Cisco layer three 3700 Catalyst and 3500 catalyst switches ,But they are just working as layer 2 devices ,all connections from Departments are just dropped in these switches ,We have PIX-525 firewall which is not in use because it does not have DMZ interface(my staff told) ,No central IP –scheme is defined e.g. some departs on 192.168.x.x some on 172.16.x.x and some on 10.x.x.x network and they get there service from Linux Squid server ,Which is multi home computer one interface is public ip and other has all these IP ranges given to interconnect all these schemes … ,So lots of traffic ,broadcast ,collisions happening ,IP conflicts ,Even people are allowed public IP because public and private network drop on same switch ,Some time public IP gave IP conflicts because someone try to gave public ip on his computer to get fast access from internet ,This is like pathetic condition ,NO vlan ,we had services like EMIAL,DNS,WEB,PORTAL .. They are all given public IP, Remote sites are also getting internet from Main site via 2 MB link, I think it is good bandwidth for these users but lots of complains of network connectivity and slow internet.
Solution
Above mention condition is very sad ,But I have to fix all this butt I need proper advise from you people, My plans are like
1-Proper New IP scheme
2-Define VLAN’s On departmental Level
3-Intervlan routing between VLAN through layer three switches
4 Redesign LAN topology
5-ServerRoom Re Infrastructure of switches /router/pix
First of all I want to design new IP scheme, like
Main site          = 192.168.100.X
Department-1= 192.168.110.X
Department-2= 192.168.120.X
Department-3= 192.168.130.X
Department-4= 192.168.140.X
Department-5= 192.168.150.X
Department-6= 192.168.160.X
Department-7= 192.168.170.X
Department-8= 192.168.180.X
Department-9= 192.168.190.X
Department-10= 192.168.191.X
Site-1               = 12.168.200.X
Department-1= 192.168.201.X
Department-2= 192.168.202.X
Site-2               = 192.168.210.X
Department-1= 192.168.211.X
Department-2= 192.168.212.X
Site-3               = 192.168.220.X
Department-1= 192.168.221.X
Department-2= 192.168.222.X
Please convey may best possible solution Step wise or complete
Thanks
Jey

Answer 1

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Thanks to all for replying specially Mr. Burleyman
So I change my plan according to your suggestion, and this is what I get
Main-HQ         10.110.x.x
Site-1               10.120.x.x
Site-2               10.130.x.x
Site-3               10.140.x.x
In Main- HQ
10.110.1.x       VLAN 1          Network equipment (routers, switches, etc.)
10.110.5.x       VLAN 5          Servers(DNS,ADC,Proxy,DHCP………)
10.110.10.x     VLAN10         Department-1
10.110.20.x     VLAN20         Department-2
10.110.30.x     VLAN30         Department-3
10.110.40.x     VLAN40         Department-4
10.110.50.x     VLAN50         Department-5
10.110.60.x     VLAN60         Department-6
10.110.70.x     VLAN70         Department-7
10.110.80.x     VLAN80         Department-8
10.110.90.x     VLAN90         Department-9
10.110.100.x   VLAN100       Department-10
In SITE-1
10.120.1.x       VLAN 1          Network equipment (routers, switches, etc.)
10.120.5.x       VLAN 5          Servers(DNS,ADC,Proxy,DHCP………)
10.120.10.x     VLAN10         Department-1
10.120.20.x     VLAN20         Department-2
     Now problem is that should I set a VLAN on switch based or building/department wise ,I am little confused here ,some departments have like 5 switches ,some have 1 ,some have 10 , and major issue for me that some departments are taking cables from other departments ,so how VLAN design will work please guide me in VLAN designing too ,I studied VLAN and configure in LAB environment ,But not in a huge network ,Please help