I guess my first piece of advice is to forget about equipment, that's really the least of your concern. I know this is the "gaffing" part of the forum, but I'll post something long winded cuz I'm bored.
The first step would be to come up with a great screenplay, something that people really enjoy reading. That is actually the most difficult part because it's very time consuming to do right and requires skills a lot of people don't have. So maybe picking up a book on screenplay writing first, will get you started on that path. Write something you can make locally without much cost. Obviously, you could have someone else write the story, or make a documentary which doesn't require the same intensity of writing. Still, anything you see on screen, is generally pre-planned on paper. An understanding how that works, is probably the best first step.
Once you've got something tangible that you can show people, the next step is to prove you can make it, which is the first step of raising money. Obviously people who have a long resume of work, don't need to do this. However, as a first time filmmaker, it's a smart idea to take your iPhone or a friends camcorder and start shooting micro projects. It's at this point I'd get a book on cinematography and lighting, this will help you understand the language of cinema. You need to experiment with this language before you can even think about making anything serious. This includes not just shooting pictures, but also understanding how audio works because that's also very important. You will also need to learn an editing software, because that's really a HUGE part of making something work well. These little micro projects show people; "Hey I can frame a shot and make something look pretty as well". That, plus your fantastic script, will get people excited and that's where money comes from. I actually shot a prequel to a feature film in order to develop the history behind my lead character.
The next step is to find some money. Crowd funding doesn't cost any money, but also doesn't make much money for projects like this. I've seen random features that looked interesting, only make a few hundred dollars on crowd funding. The projects that succeed at making a lot of money, usually have big backers already attached and they use that money to help boost their crowd funding chances. It's a commonly used trick and it works well. So unless you have a long lost aunt or uncle who are willing to back your film with a few hundred grand, you can probably forget about making enough money to properly fund a serious project with crowd funding. So your money is going to come from friends and family, $20 here, $50 there and you'll probably have a budget of a few grand when it's all said and done. Between me you and the wall, the only thing you really need money for is expendables (tape/gels/hard drives to store your media, etc) and of course food. If there is one thing that makes people happy, it's food. You're job as a filmmaker isn't to make a movie, it's to make sure your crew is well fed.
On films that actually have a budget, you would budget things like art/props, lighting/gaffing and camera/sound equipment rental. However, with something small like this, your "budget" is whatever you can acquire, which maybe a lot or maybe nothing. So what equipment you use, is really dependent on how much money you make, not the other way around. Guerrilla filmmaking is kind of what you'll be doing and part of that is being very clever, as you said earlier, with building/making your own bits and pieces to achieve certain shots. Lights would be the first thing I'd focus on and those old style aluminum work lights with the reflector behind the bulb, they work great. Just need some filtration and a bright-ass bulb and you're in business. Pretty much everything you need for production will be available to you at yard sales or goodwill stores.
Now comes the shooting equipment, camera/lenses and sound. Most people shoot digital today and I would suggest doing just that. Yes, it would be awesome to shoot everything on film, but once you learn about the expenses involved; (raw stock, processing, transfer) you'll find it to be cost prohibitive, even with small-gauge formats like Super 8 and 16mm. Now, that's not to say it's impossible, I've made micro budget 16mm films for years, but we had our own camera, sound and lighting equipment. We were donated film stock through a Kodak program that's long gone and I found 50 rolls of film at a garage sale that was still good. We got killer lab deals and one light telecine, which gave us something watchable. Now I see your a student, so perhaps borrowing equipment from school is your ticket to success. If you can't and you need to find cheap stuff locally, I'd put an add on craigslist to see if you can find a cinematographer locally to supply you with equipment. You can also try www.sharegrid.com, which is a great place to hook people up with equipment.
As much as I love film and am an advocate for using it, you need to analyze your financial situation before contemplating. Digital is practically free to shoot (once you have equipment) and as a new filmmaker, you will see instant results to insure you've got the shot before moving on. On no-budget films, this is awesome because you can prove to yourself, you've got it in the can. With film, you could make a huge error and not know about it until that 12 minute roll is processed and digitized at an expense of around $500 (stock, processing, telecine, storage). We have these great digital tools today and for your first big short film, I'd use them. Ohh and don't ever forget about audio. You need at least a 4 channel recorder, wireless mic's on each person and at least one boom mic, with an operator. Just remember, one wireless and one boom per person in the scene. Record only in silence and make sure it sounds good before you move on to the next shot. Assume you will never get the actors back for ADR (automated dialog replacement) because you won't and if your audio sucks, you will not have a viable product. I always wear a set of wireless headphones on set, listening to the audio on my digital shoots because I can't afford to re-record anything.
Cutting picture can be pretty easy, you can read about how to cut properly in books and watch lots of movies. Audio is the difficult part and it's hard because it's A LOT OF WORK. There are great online resources for things like effects and music, you will need everything you can get for free and make sure you jot down where you go it from so if your film does make it somewhere, you can pay the royalties. I suggest www.freeplaymusic.com and www.royaltyfreemusic.com to start with. Effects can be purchased on CD, but libraries are online as well, so I'd just do some google searching OR if your lucky, your school may have something as well.
Ohh and one more thing… When I was a kid, all I wanted to do was make movies. So I saved up and bought a super 8 film camera, back when consumer video cameras were very expensive. I spent years learning my craft, experimenting with the medium, cutting it by hand, projecting final products, even if they were complete crap. I do think there is a lot of learning that can be had through just experimenting. Buying a Bolex 16mm camera, projector, splicer and viewer. You'd learn quite a bit about film and you may make some great products. However, that's an expensive first step and it will take a while to make an acceptable product. I wish the digital cameras we have today, existed back then because I could have afforded them and shot a lot of great stuff without the expense of film. I do love celluloid, but digital is the great enabler, so you should embrace it and make your film.