This is a great time to get into filming or photography with so many cameras available with various great features and price points. There is nothing stopping you learning to shoot as the phone in your pocket has a full hd video feature already. However if you want to get into the next level of creativity and quality, a great first investment is any Canon DSLR with a large sensor (550D, 60D, 5D mk2/3) and a full HD (1080p) video function.
The reason I strongly recommend buying a DSLR is that there is a challenging learning curve for shooting video and this will teach you to learn about audio, focus, stabilisation, lenses, lighting and framing. Everything can be manual and the results are obvious when you get it wrong but can have the awesome factor when you get things right.
DSLRs are versatile and discrete however if you just want to start shooting with the most conveniences and don’t mind having the look of small sensor video. Hey, let me tell you, shooting events with shallow depth of field isn’t always fun. You can always buy a small chip camera and they certainly have their place for fast pace shooting environments or where you may need an electronic zoom and an all in one reliable package.
Another plus of buying a DSLR is that you have an excellent tool for high quality photography and time-lapse. Keep in mind when you buy the camera body that it is only the beginning of finding the accessories that suit your shooting situation. The internet is a brilliant place to find out information on gear and how it may or may not suit your shoot or budget.
There is no right or wrong way to go about purchasing your camera, you have to ask yourself what sort of work would I like to shoot? Then once you start shooting the work you end up doing can vary vastly and in most cases as your skills and experience develops so does your gear.