The market is so saturated with cameras it is almost impossible to decide which is right for you. There is almost as deep a pile of review sites giving you their version of what to buy. This article in The Telegraph at least tries to cover the full gamut in camera type and price
The best point-and-shoot cameras on the market, for everything from cheeky selfies to heavy-duty travel photography

Sony Cyber Shot RX 100 II, available in black, RRP £649.00
For a camera with so many intricate settings, the Cyber shot RX100 is surprisingly easy to understand. As you scroll between the major modes (Auto, Aperture Priority, Macro and so on), a sentence on the screen will appear to tell you what that program does and when you might use it. There’s also a handy spirit level to show you when you’ve got the camera completely straight.
Once you are in and shooting, there is even a “help” button which brings up practical advice on capturing difficult subjects: dusk, for instance, or the greenest leaves.

Panasonic Lumix DMC-FT5, available in black, blue, orange or silver, RRP £249.99
It’s sacrilegious to compare anything to a Leica; but it’s also an open secret that Leica’s digital lenses are made by Panasonic. If you dream of owning a digital Leica, complete with famous red-spot logo, then you’ll have to set aside at least £500. But if the quality of the photograph is what matters to you, you can get your Leica lens for less with a Lumix. It’s what quite a few professional photographers carry around with them

Sony TF1 –available in red, black and blue, RRP £140.00
This relatively cheap camera is slim and light and sits easily in the hand, with rubberised edges to keep your grip secure. I was initially befuddled by the placement of the lens in the top-left hand corner of the camera – which is where I suppose you would expect to find it on a cameraphone. But with a largeish screen, when your finger strays into shot, which it inevitably will, you can see it and readjust accordingly. The zoom button on the top of the camera is ridged, which makes it easy to get hold of; the zoom is internal, not telescopic, which makes it more robust – if you dropped it, there probably wouldn’t be dire consequences.
See the rest of the reviews of these cameras and the others recommended here