Best Camera for my situation?

I have an IPhone and an 8 year old camera that was like $50, and thats all I have to take photos with. I decided that its time for me to get a good camera and really capture the moments in life beautifully. On Facebook I see my friends and family posting these amazing clear photos, and I want to get good results like theirs. They are no professional photographers, nor am I, and don't know much about photography or editing. I'm going to Europe in a couple weeks and want to take really good quality, clear pictures. I don't want a big bulky camera, just something that will give me good clear pictures. I don't want to spend more than $400. I would like to frame some of these pictures, so I do want the best quality. Again, I'm not professional and don't know much about photography.

Check out the FujiFilm x10/x20. I'd highly recommend the x20 even if it cost a little more and may be out of your price range. I promise you won't be dissapointed.

I would recommend a Nikon l520 or a Canon SX40 or equivalent type bridge camera. A bridge camera lies between a Single Lens Reflex (SLR) and a point and shoot compact, carrying some of the benefits of both with a price range to match. An entry level SLR, such as the Nikon D3000 is in your price range, but I'm thinking of the need for lenses, the ease of use and the bulkiness compared to a bridge cameras. A bridge camera offer wide angle shots, taking the whole seen in, or super zoom to fill the frame with a single detail, one would need a whole bag of SLR lenses costing thousands to compare.

With digital cameras its all about the sensor, two things to look for:
1) the mega pixel value; this relates to the amount of information the sensor captures.
2) the actual size of the sensor, this relates to the ability of each pixel to capture the available light without interference, which shows up as noise in the shot. That's essentially the reason why a 12 megapixel compact couldn't compete with a 12 mp SLR.

Digital camera technology moves forward like all digital technology; the latest product is usually the best, better than the previous model.
I would recommend you enrol in a photography course, find the cheapest 6 week course in your area. You will learn loads from been around people with a similar interest, also, you'll learn how to use your camera and also something about what constitutes a good photograph.

Do your research, posting the question was a good start. Go into your local camera shop, tell the dude you've got 400 bucks to spend, your going travelling, what's he/she recommend. Before you buy, go on line, do some research (snapshot website as very clear comparisons across nearly all brands and models), then if what the dude in the camera shop was saying rang true, go back and spend your money.

Good luck, photography is a great joy and worth putting effort into.
For editing start of with Google Picasa, after you get a hang of that, move on to one of photoshop type editors.

You can take great pictures with certain compact cameras these days. You just have to pick the right one!

Canon's PowerShot SX260 is a good buy, especially since it's last year's model so it should be pretty cheap. Otherwise, the Sony HX20V takes great pictures too.

If you're looking for something more advanced, the an interchangeable lens compact is a much more compact solution than a full-sized SLR. Sony's NEX range of cameras are particularly good.