I am a retired LAN/WAN Network and Hardware Help Desk Manager for a US Federal Agency. I had both Level 1 and Level 2 Help Desk techs working for me and also contractor LAN engineers (originally Novell CNE's and later Microsoft certified Engineers) that could be consdered Level 3, although in our system the Level 3 support was mostly Computer Analysists at our agency's national computer center headquarters.
A lot of what you need to do depends on which direction you want to go - operational or hardware support. If it's network operations and administration then you need to become certified in whatever system the prospective employer uses, such as Microsoft for Microsoft client server systems and maybe even some programming knowledge. If it's hardware then obviously you need to have some formal hardware training to break into that area and along with the PC's you will need router, modems, etc.
When we started our networking and help desk, it was in the early 80's and everything was new, thus all my HD Techs were mostly on the job trained. Some of my HD Techs came from an electronics background, some from communications background and some were mainframe computer operators, but since this was a new career field we couldn't send them for any type of formal training. I did have in-house training that I did myself - in specific areas as needed.