I can only agree with what has been said so far. Go digital, partially for the instant feed-back but also for the fact that shooting is almost free. With film you're far less likely to experiment or take risks because you pay for every shot twice; once when you buy the film and again when you have it developed. Then if you want your images to be in digital format so you can post them or e-mail them, you have to have them scanned or invest in a scanner. And even if you already have a scanner, the process for more than just a few photos can be mind-numbing.
I also recommend that you go for an SLR. The reward can be many fold what you get with a point and shoot and even though you can use it much like a point and shoot by sticking to Auto and/or Program modes, there is so much more you can learn and do. Among the biggest differences for me has just been the immense increase in satisfaction. Even though my point and shoot cameras took pretty good photos, it was rare to see a breath-taking image and be able to capture anything but the technical aspects of the scene. You could tell what it was, see the colors and understand the concept, but the dynamic range of the image just wasn't there. With my digital SLRs, the result is quite often just the opposite. Sometimes a mundane looking scene is captured in such minute detail, with such accuracy, that the resulting image is far more stunning than the original.
Buy a point and shoot if you just want to study concepts like lighting (which will be limited), or composition. If you want photographs you'll want to share and view time and again, then do whatever is necessary (including stretching your budget), to get a nice entry-level Digital SLR.
Get one with a reasonable kit lens if you can, then as you can afford it, add to your lens collection. Each new lens will change the personality and expand the capabilities of your equipment. Then you can get a flash, macro, filters and all of the other accessories that let you put your own creativity into every scene you choose to shoot.
As for landscapes, you'll probably want a decent wide-angle lens. But don't get the idea that wide-angle is the only way to shoot landscapes. I've seen some brilliant work done through creative use of telephoto zooms. My personal favorite is macro. As much as I love the idea of photographing wildlife, I wouldn't be happy coming home with one decent photo every month or two and wild animals just aren't that easy to find and photograph. With my macro lenses, I can always find a bug, a tiny flower blossom or just some diminutive tiny corner of the world somewhere that most of us over-look every day, and turn it into a macroscape of wonder.
With a good D-SLR, the possibilities are nearly endless and you'll learn much more quickly because you don't have to check your wallet before depressing the shutter release.