Infrastructure is a generic term referring to the stuff most non-IT people never see, mostly the network and servers. A user goes to website.com, and a pretty page is displayed in their browser. What is not seen is the workstation needs to find an IP address for website.com (DNS server), then the request needs to go off network (switches and routers), across someone else's network (WAN provider or Internet), to the target network (switches and routers), and finally to the server that houses the code for website.com. All of that is infrastructure.
I haven't played in the server space in many many years, so I don't know what the hot certifications are, but I would assume Microsoft or Red Hat are still sought after. Cisco, Aruba, and Juniper are good network certs.
The certs are really to get you past HR. Once you are in a technical interview, it's all about what you can actually do. For instance, a CCNA will show you have the skills to do basic configurations of Cisco switches and routers. But that does not mean you actually know what the switch or router is doing. For instance, I can teach a monkey that all access ports need the "spanning-tree portfast" command. But the monkey does not understand why. What is spanning tree, why would I want it on or off?
Half-price books has tons of used cert books. I would go get three:
MCP - Microsoft Certified Professional
CCENT - Cisco Certified Entry Level Technician
RHCSA - Red Hat Certified Systems Administrator
Read these and decide if any excite you. They are big ass books, no need to read cover to cover.
Does that help, or did I completely miss the question?