(Warning: Long post ahead.)
If you haven't already done so, make sure you master basic networking such as wired and wireless LAN technology, and all things IP. It may be tempting to skip this and just concentrate on the OS, but starting off with Linux administration (or Windows, for that matter) without knowing the details of the underlying network protocols would, in my opinion, be a mistake. Without this knowledge, you would be more likely to make silly mistakes (some of which could be security related), and you would probably find troubleshooting the network a tedious and difficult affair.
Topics covering LAN technology would include:
- basic Ethernet theory (transmission and addressing)
- switching
- the Spanning Tree protocol
- VLAN/802.1q
- 802.1x and RADIUS
- standards for copper and fiber cabling
- the various 802.11 (wireless) standards
Knowledge of basic IP theory is also vital for any network admin:
- IPv4 addressing and subnetting
- IPv6 addressing and subnetting
- routing
- the most common interior routing protocols (RIP and OSPF)
- the TCP and UDP transport protocols
- common application-layer protocols (HTTP, DNS, SMTP, SNMP, FTP, SIP etc.)
- firewalls and traffic filtering
- network address translation (NAT)
- SSL, TLS, certificates and PKI
- VPN protocols like IPsec and L2TP
These are topics covered by several certification exams such as CompTIA Network+ and Cisco CCNA. You could get one of the many certification-oriented books available, and perhaps consider taking an exam as well. The CCNA exam was just given an overhaul, and it's actually looking rather good.
As for teaching yourself Linux, you should focus on getting as much hands-on experience as possible. Set yourself a few goals, such as installing Linux and configuring a web server, a mail server, a file server and so on. If you're currently a Windows user, you could start by installing Linux in a virtual environment such as
VirtualBox.
A Linux admin will need to master such topics as:
- installing the OS
- keeping the OS updated
- installing and maintaining applications
- creating users and assigning permissions
- troubleshooting applications and data flows by analyzing logs and reading debug information
- securing the OS and installed applications
- setting up a centralized or distributed authentication service (including AD integration)
- managing storage
If you're starting from scratch, you could do worse than reading up on the CompTIA Linux+ curriculum.
As for books,
Running Linux is considered a classic. I rather like the
Sybex Linux+ Book, as it's distribution neutral and reasonably up to date. It's not fantastic, but I would say it's good for teaching the basics. Your distribution of choice will also provide documentation that could be of value.
I don't have any recommendations for Network+, but for CCNA I'd go with the official
Cisco books by Wendell Odom. They are rather expensive, and many would recommend the Sybex book on the topic, but to be honest I think it's quite bad. Wendell Odom is meticulous and may seem a bit tedious at times, while Todd Lammle is all over the place, bursting with enthusiasm but lacking structure. Anyway, right now the Sybex book hasn't been updated to cover the new exams.