What kind of digital camera to buy?

I'm looking at getting a new camera. Right now I own a Cannon point & shoot camera (Power Shot A480).It has 13 time zoom with a bunch of little extras like scene selections, video recorder, timed flash, B&W photos, etc. However, I have always envied the SLR and now that I live in China, I get a Nikon for as little as $250 USD at a reputable store (not a market). They also have Sony, Fuji, and Minolta. I don't want something that I will have to get a PHD to be able to operate, but one that gives me better quality and better zoom options and better all around picture quality with maybe a few extras. I'm not the world's greatest photographer, but I enjoy taking pictures immensely and would love to be able to go up in rank as far as photography goes. I want to be able to take pictures that look like someone that knows what they are doing has taken them as opposed to just an amateur that takes household pictures of their pets. Can anyone help me decide what is the best camera to get for an amateur striving to be an advanced photographer?

Added (1). I already have the Cannon Powershot A480, and while it is a good camera, it is not up to my liking as far as amateur photos. The 2 I have immediate capabilities to buy are:

FujiFilm S1770 Finepix with 15X optical zoom. It runs about $235 USD.

Olypmus DC SP60 with 15X optical zoom. It runs about $260 USD.

I really liked the Olympus because it has a built in tutor on the menu options and allows you to be able to go through each option as it teaches you to use each one.

You won't get "better zoom" from a DSLR as the basic kit lens (18-55mm) is an equivalent 3x zoom in compact camera terms. To get something more you would need to purchase a lens suitable.

You might want a bridge camera. Something like the Fujifilm HS10 offers massive zoom (30x) as well as some manual controls you typically find on DSLRs. That way you get the benefits of single-all-in-one solution of a compact with handling more akin to an SLR.

http://www.fujifilm.com/...epix_hs10/

***EDIT***

Looking at your budget then I could also suggest

FujiFilm F300EXR - wide angle, 15x zoom, 12, 800 max ISO, panorama 360 and HD video
Pentax X90 - 26x zoom, TRIPLE image stabilisation
Lumix DMC-FZ35 - 18x zoom, Leica lens, AVCHD movies