OK, I will get the ball rolling. Ghost hunting on a budget? try this for starters:
Disposible camera
thermometers (preferably more than one)
tape recorder
video camera (at least one person in the family usually has one, borrow it! lol)
notebook and pen/pencil
something to eat or drink, depending on how long your vigil is
I think this is a good starter, and aside from the disposible camera, everything else can usually be borrowed from friends or family members.
Also, make sure you do your research, find out where the 'hotspots' are, maybe even go to your location a few days before to look around, get your bearings, make notes as to any hazards, interesting features, general layout etc. Maybe even ask a few locals about whether they know about anything.
Important note: ALWAYS ASK PERMISSION! don't just assume that your presence will be welcome by the living, let alone the dead. If you need to go on private property of any kind, always ask. You will find that most people are very accommodating, as long as you're not being a nuisance and you clear up after yourself

Also, as an aside, always dress appropriately, especially if doing an all-nighter, the temperature can change quickly, and you dont want to be freezing your proverbials off...
I always recommended taking at least one other person, not too many people mind you, as that can detract from the situation at hand. Not only does it help to verify anything that may happen, but also you have help if there is an accident etc etc etc.
Good for a start???
Gigan