A few considerations:
What you need is going to depend a lot on what sort of work you're going to be doing. There are two main ways of working--using a field mixer that plugs straight into a camera or "double system" working that involves a separate recorder like a Zaxcom the will sync with the camera. The Zoom is probably not suitable for either of these methods of working so you'll need to analyse your potential clients carefully and come up with a decision on what you need to buy.
For microphones, the bare minimum will be one short shotgun and probably at least 2 portable radio microphones (the sort with battery powered receivers at your end). Three or four radio mics wouldn't hurt. If you're doing news or current affairs work, something that can be used as a handheld mic is often asked for.
For your shotgun, Sennheiser is industry standard but the Rode NTG 1 or 2 are very good mics for a lot less money. I used to carry one as a backup for my Sennheiser 416 and the people back in editing never noticed the difference if I swapped. (I'd probably go with the NTG 2...it's the same mic but can operate either with phantom power or on it's own internal battery, something that can be a lifesaver when the shit hits the proverbial). Whichever mic you choose, you'll need a good shock mount and a wind shield. You'll also need a good, long fishpole. Don't skimp on the fishpole and get a strong but light one. Cheaper ones weigh more and believe me you'll be grateful you spent the money at the end of a shot several minutes long.
I won't recommend radio mics because you'll have to consider legal frequencies where you might be working.
A general thought...I know you want to be as cheap as possible but, except for the world of wedding videos and the lowest of low end corporate, you're probably going to need more than a student budget would allow. I'd seriously suggest you might want to try and get work as a sound assistant where you don't need to provide your own gear, both to get some experience and also to get an idea of what work you want to do and what gear you want/need.