That’s like asking if you’ll be guaranteed to shoot a deer if you’re going hunting. You just don’t know if you will or not, and you have to be willing to take the chance that you’re not going to get one.
With ghosts, you may or may not be able to record one on a digital camera – though I retain the stance of being neutral on their existance, I’ll pretend I think they do exist for your sake. Many people have captured ghosts on photographs and video, or at least what they claim are such creatures. I’m sure the same applies not only for traditional cameras, but for digital ones as well. Be careful when taking pictures – if you use the flash, it may illuminate particles of dust which will end up looking like ghostly “orbs” or whatnot.
Also, remember to remain skeptical until you have definitive proof that there is something unnatural going on in your home. If you think that you have ghosts in your house, you are going to see them everywhere, and in everything. Once people start believing that they have ghosts, everything becomes the ghost – if a window slams shut, it’s the ghost. If the keys to the car go missing, it’s the ghost.
99.99% of the time there are alternate explanations for what is going on in a home. Carbon monoxide poisoning can cause hallucinations and paranoia. Powerful drafts can cause doors to open and close – when I first moved into the house I’m in now, I was scared as Hell when I left my bedroom door open and it slammed shut VERY hard when I was in the kitchen. I soon figured out that it was opening and closing because the window in my bedroom was open, and the circulation of air was forcing it shut. You may have something else wrong in your house.
If you were at a haunted cemetary, your mindset will also be one of looking for ghosts – you wanted to see ghosts, you have ghosts on your mind, and all of a sudden they seem to be in your home. Dark shadows, especially those in your periphereal vision, often aren’t specters. They’re just figments of your own imagination – a question for you now: did people start seeing these dark shadows one by one, or did one person see a dark shadow, and then everyone started seeing them? Because the human mind is a very fragile and imaginitive thing… If somebody tells someone of a gray ghost on the staircase, that person may see it simply because they expect to see it.
Anyway, back to your question.
If you are planning to use the digital camera to tape for long periods of time, you better plan on having a LOT of storage room. My digital camera, with a few photos on it, only has room for about an hour of recorded footage. You can buy pinhole cameras for only a few dollars and set those up and have them connected to a recording unit.
If you sincerely think there is something weird going on, pay attention to your pets, if you have one. Dogs and cats seem to be more sensitive to paranormal going-ons that people – if there is something strange, dogs will perk up and look at spots on the wall or bark at nothing. But always remain skeptical! Your dog could just be hearing a distant thunderstorm and getting nervous about that.
EDIT:
I wouldn’t take Lovro’s suggestion of immediately uploading your video to YouTube, unless you want to be ridiculed by everyone there. Most ghost videos on YouTubes are either well-made or poorly-made fakes, and putting a video on there only gives the impression of you being an attention seeker. So I wouldn’t do that unless you get something that is definitive, clear, and shocking – which in all likelihood, you won’t.