Hi all. This is my first post but I've been addicted to TE for a few months now. It's been really helpful for advice while I'm pursuing my career in IT

You guys are a really great community!
Today I finished my first day on the service desk that supports a semi-national company. It's a 6 month per day contract. I'd like to form a plan on how to use this current job as a spring-board, but I'd like your help.
The definitions of Help Desk are broad and varied so I'll just list what I observed the woman I shadowed do:
+It's a first-point of contact
+They have 2 virtualised desktops for each of the two parent companies. One uses AD 2008 and the other uses 2003.
+The employees we support use a Citrix-based platform for their access portal (I think, never encountered Citrix before)
+We log and assign tickets using a website that's tied in with the system
+Total user size is pretty big, multi-sites in the country. I'd say 1000-1500?
+I observed the woman use AD to unlock accounts, reset passwords and various
+Seems like a large portion of the job is issuing requests (like a mailman); Deskside Support go here, XYZ support call this person, ABC do this task etc
+Support field engineers and their devices
+The emails need to be answered with 3 hours and phone-calls are to be kept >5 in general
(Good work atmosphere but it seems very very busy. Seems like a great place to cut my teeth.
I'm also deciding whether to pursue an MCSA in Server or go for the CCENT. Still trying to figure out which side of things I'd like to do.
I'd like to know how I can leverage my job to learn more skills and tech? Once I can do my actual job description of course!
I've read asking for more duties is an option or show you're willing to learn.
What is the best way to do this in a very busy environment - one where you don't really get any down time?
Examples would be great!
There seems to be potential for branching out into a Desktop/Field Engineer path. Should I consider this? Is a Desktop Support much of an upgrade vs Help Desk?
There's also a NOC upstairs which I would LOVE to sneak my way into as I think it's a perfect balance of stuff I don't know vs stuff I can learn and be useful. I think I'd need to do a combination of really buckle down and achieve a cert as well as display to my supervisor's supervisor a willingness to learn.
My background: I'm trying to get into IT, with not much working experience; daily user of computers since a kid, some part-time work for my Uni tech support for a year. Not that they count for much, but I have also passed 4 of the MTAs for Infrastructure (server, networking, security and os fundamentals). They were free and gave me something better than 'good with computers' to put on my CV.
The past 6 months I worked in a call centre. I could say I learned soft-skills and troubleshooting, but to be honest I already had those skills. At best I did something a monkey can do. However, that said, I did consistently make very strong connections with strangers over the phone (people sharing personal stories, facebook/email contact etc) that I have empirical 'proof' of.
The most advanced stuff I did, outside of the product, was conference call customers' ISPs. We werent encouraged to do this, but I did it anyway - we all know how Reps try to baffle normal every day users. So I guess I did some tertiary network trouble-shooting.
[Record was a 4-way conference call and a 5hr 30 min call]