There are five possible methods that I can think of:
Tethering to a Computer
You can connect the camera to a computer via USB. However, this limits movement and can be inconvenient at times. This also requires specialized software. This is the cheapest option by far. You will still need a conection to the internet.
An Eye-Fi card
The second cheapest method would be to get an Eye-Fi card.They do not require the camera to have Wi-Fi and are able to link directly to social media. This, unlike tethering, allows you to move around without restriction. However, there must be a WiFi network present.
A compact camera with WiFI
Some compact cameras have a built-in upload to the web feature that doesn't require any further equipment. Many of Samsung's cameras have this feature. Nikon and Canon also have cameras with built-in WiFi. This would give you slightly more control than the Eye-Fi cards. This gives you the same range of movement as the Eye-Fi, and also requires a WiFi network.
A smart camera
Finally, both Nikon and Samsung even have cameras that run Android. They can then run photo apps, giving you further options for upload. This is more expensive than the previous options, but gives you the most control. Another benefit is that both of these can connect to cellular towers, giving you connectivity in places without WiFi.
A DSLR with WiFi
For the most photographic control and best photos, I would reccommend getting a DSLR. Some come with built-in WiFi. If you have one already, there are accessories that will work with the camera. Most can also accept an Eye-Fi card.
I hope that this helps.