This depends a bit on the size (that means budget) of your company.
The most basic concept is to have two VLANs at each site. One for servers and one for workstations.
You start by putting all the switch ports into the workstation VLAN, and then as you plug in a server, you move that switch port to the server VLAN. This "concept" is what the vast majority of companies use. This doesn't require you to have any network engineers on staff and can be managed by a local IT team.
You can step it up using things like 802.1x with RADIUS (such as Cisco ISE) and authenticate devices as they plug in and automatically move them to the correct VLAN. A small percentage of companies do this. By this stage, your company probably has IT team members with strong networking skills but maybe not big enough to employ dedicated network engineers yet.
You can step it right up and use a switch that supports SGT with Cisco ISE. This allows Cisco ISE to say what the user can access precisely. It costs a lot. Used by only a very, very small percentage of companies. At this scale, the company is likely to team an internal team of network engineers.
What kind of kit to consider? It depends on the bandwidth required between the users and servers.
For example, an MX250 security appliance can route around 4Gb/s. If that is enough, then you could use an MX250 with more basic layer 2 switches.
https://meraki.cisco.com/product-collateral/mx-sizing-guide/?file
Otherwise, you are going to need to look at layer 3 switches. This will depend a lot on your site, but you might look at MS250's and above for the core switches (I also personally like the MS350-24X and MS425-16's) and maybe MS225 switches stacked together for your access switches (this depends hugely on the number of users at each site).
https://meraki.cisco.com/product/switches/stackable-access-switches/ms250-48/
https://meraki.cisco.com/product-collateral/ms350-series-datasheet/?file
https://meraki.cisco.com/product/switches/aggregation-switches/ms425-16/
https://meraki.cisco.com/product/switches/stackable-access-switches/ms225-48/
You will want to get a Cisco partner engaged in helping with proper equipment selection and network design.