1) It depends. Know the OS well if you want to be a Windows-based system administrator, Exchange admin, sharePoint admin, SQL Server DBA, etc. So much of how those apps work is based on the OS. So get very comfortable with the desktop OSes Windows XP/Vista/7. And learn Windows Server 2003/2008. There's a huge 2003 install base that won't be migrating very quickly.
2) Don't just depend on certification books and sites. They won't give you the all around knowledge you're going to need. You're going to need to pick an area to concentrate in, and that really determines the site. For instance, on the SQL Server side, the first place to start is SQLServerCentral.com but there's a ton of other sites like SQLBlog.com, SQLTeam.com, SQLServerPedia.com. TechNet is a good site. Books? The how and why books that have been mentioned. And then focus on the subject you want to go into the most. You can generally use Amazon and other sites to get a feel as to what books are good. If you want to save some money, check out library sites like Safari (safari.informit.com).
3) This depends on the area you want to focus in. Probably your best bet to get in the door is as help desk/workstation support. In that case, A+ and MCDST are the first couple of certs you're looking to work as you gain experience. But as they say, certs aren't everything. You want to build up experience and couple that with your certs.
4) Most folks that get into system administration either start by doing it on the side, or by coming up through help desk or something similar. In your current organization, if you can lateral over to a technical team, that would be the most ideal situation, especially if there is time built-in for you to come up to speed. Otherwise, start looking for helpdesk and junior admin positions. Be honest with those interviewing you. If you have strong people skills and show a willingness to learn and be a team player, they may be more willing to take a chance on you than someone more experienced.