To optimise network connectivity for this requirement can be even accomplished by
Router : 1 (example 1800 series) or any high end router,
Switch 1: layer3 switch (example Cisco 3850) or any other vendors
Switch 2: layer2 switches depends upon number of end users and servers hosted
Configuration SVI in layer3 switch number of SVI configuration depend upon business requirements among this SVI one VLAN can be used for management for accessing layer3 switch and layer2 access switches . DHCP can be configured on layer3 switches for dynamic allocation of ip address to end-users. Use static addressing for DMZ VLAN. Restriction among VLANs can be controlled by a access-list configuration in layer3 . Connect access -switches with trunk links from layer3 switch . One layer2 switch is deployed in 1st building , second layer2 switch in 2nd building . Layer3 switch and router will be deployed in 1st building . If distance between two buildings are above 100 meters then use fiber cable for connecting layer3 switch to 2 building access-switch use media convertors at both end for ethernet to fiber convertors pupose if not go with sfp modules at layer3 end and media convertors at layer2 switch end.
Configure default route in layer3 switch pointing towards router inside interface .
ISP internet ip should configure on router outside interface and configuration default routers in router
Assuming LAN supernet address : 10.180.0.0/19
Ip route 0.0.0.0 0.0.0.0 point towards ISP gateway
ip route. 10.180.0.0 255.255.224.0 pointing towards layer3 egress interface /*connecting router and layer3 interface
Configure natting in router for internet access and static natting for accessing application from outside both for inbound and outbound traffic
Even firewall can be used in place of router as per your requirement
If your setup wants to access any other DC resources from point to point link you can have feasibility connectivity from layer3 as L3 interface and configure static routing both ends.