How to reduce traffic/broadcast traffic in a supernet network?

Our network has grown in size with desktops, vDesktops, iPads, and servers. We are in a class C subnet mask.
We implemented 255.255.252.0:
x.x.1.1-254
x.x.2.1-254
x.x.3.1-254
x.x.4.1-254
Our company is growing as well as the devices.
I was hoping to do some subnetting because network performance is not the same.
From what I read about subnets is that you can break a network to smaller components to reduce broadcasting traffic and increase performance.
I was thinking about breaking down into subnet the different types of devices, such as:
Servers
Printers/Appliances
Desktops (into two different subnets)

What steps should I do for a successful implementation?
What precautions should I take not to damage the network?

We have 6 level-3 switches, each with 48 ports.
In this implementation we can use three of them, those are not being used. Still in the box.
Yes, they are managed switches.
We have two NAS(8 nic ports each).
We have four host machines(7 NIC ports each).
We will be adding another host within two months.
We have about 10 devices, each with one or two nic ports.
We will be adding a new backup device from Barracuda next month.

We run in a VMWare virtualized environment(75% at this time).
We also run our vDesktops from VMware horizon view.
To complement that we use Unidesk as well.
We have two DCs, one is for failover.

How should I start the breakdown?
What is best route for best network traffic?
j_ramesesInfo Sys MngrAsked:
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JustInCaseCommented:
Recommended max IP hosts per broadcast domain is 500 (but it can be too much).
How to start breakdown - usually it is better to create VLANs per logical group (like  department). Servers, Accounting, IT, Guests etc ....

For start you can enable portfast (if it is available on yur switches) to all ports that are connected to end devices, that should help a lot if portfast is not already configured on switch ports, however that is temporary fix to reduce broadcast storms.

First you need to know what network design you want.
Do you want redundancy in your network or not?
Get the most powerful L3 switch (if you want redundancy than take two) that you have (or buy some) and enable ip routing, create necessary VLANs and vlan interfaces (on vlan interfaces you should configure ip helper-address so devices can get IP address), create default route, and set that one as root bridge. Then you need to decide will all inter network traffic be allowed, or you want filter network traffic (so users or vlans can access only specific devices on specific ports).  Than save and backup config to flash. When that is done you can start attaching switches to L3 switch and creating vlans on them, then you can start migrating hosts and IP addresses (also you need to reconfigure DHCP server). You should choose IP address range so IP range can be easy to summarize...
There are many more details, but you should start with network design, how network topology should look like, than according to that big picture you should insert small parts and solution for each one.
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j_ramesesInfo Sys MngrAuthor Commented:
Thank you Predrag,

We will be setting up our L3s as well as several vLANS.
We will stay away from supernet.
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