Well it all depends on how much you want to spend on a camera. Many people who are into independent film) go for photo cameras which also shoot HD movies (such Canon T2i, 5d, 7D, or other cameras by Nikon, Panasonic, Sony, etc.) This is largely because this is the cheapest option, because of the use of cards instead of tapes. However even though some photo-camera claim to shoot 1080p60 quality video, do not believe it, stick to the cameras that shoot 720p30.
If you have money to spend, you can always invest in a camera from either RED Digital Cinema (RED ONE or EPIC, or SCARLET which range from $11,700-$58,000) or an ARRI ALEXA (which is $60,000) but I would only invest in these cameras if you plan to make an actual movies (the RED SCARLET is the cheapest on this list.)
Sorry if this list is very broad, it's just that there are may cameras on the market today, and each one has a special purpose, and It's hard to tell what camera is right for you. If it's just home videos you plan to make I high suggest checking out a Canon PowerShot SX130IS 12.1 MP Digital Camera with 12x Wide Angle Optical Image Stabilized Zoom with 3.0-Inch LCD. It shoots 720p HD quality images, has a 1/2.3" CCD sensor, and it's relatively cheap (about $134 on Amazon). That's just my opinion anyway, hope this answer helps.