Well it depends if you intend too take the hobby more seriously or not.

If you pretend to make it at an amateur level, i simple compact camera won't be suffice, but if the intention is just to take an occasional picture, then maybe your cell phone is enough.

That being said, the point is, compact cameras like Canon PowerShot SX260, just for example, don't had much more at the thrill of taking a picture than your Galaxy SII.

That being cleared, next step is, a bridge or a reflex DSLR...

The reflex would be always a good option if you intend to be in love with this hobby, like the main hobby where you spend all the money granny and family give at xmas. Doesn't depend much of the camera, but more of your skills, with a reflex you can do amateur or pro stuff, and it's a good camera to switch from one state of technique level to another.

The bridge camera, is something between a compact and a reflex, but for me depending on the brand and model of the camera, it's more similar to a reflex with a fix lens, than to a compact camera, the experience i mean is more similar to what you get with a reflex, but it still has that noob automatic knick knacks that help you to start.

In my case i started with a Nikon D90 and 3 or 4 lenses, but it's a bit expensive, so in your case i would say for you to get a nice bridge camera like a fujitsu, or olympus, and start with that. You'll get some of the feeling of a more serious camera than a compact or a cell phone, and you'll be able to improve your techniques faster, because with a compact camera is point and snap, with a bridge is a little more than that if you want to, but it can also be just point and snap.

So in your case i would choose a bridge camera like Sony Cyber-shot DSC-H50 or Fujifilm Finepix S100FS.

i have both, here at home, and can tell you that they are pretty cool cameras to start with.