You need to know what the lens on your point and shoot is before you start buying. That way you can say I have xxx mm and I want more. Small cameras have tiny sensors and don't need huge lenses to get the telephoto effect. The bigger the sensor the bigger and heavier the lens need to be to get the same reach. You may find that just the lens to get the reach you have now is going to be much larger and more expensive than you think.
Cramming more and more megapixels onto a sensor is a advertizing trick. Kind of like having a car that does 400 MPH. You will never need it but isn't neat that it will. Realistically 5 mp will print as large as most people will ever need which is 4x6 to 8x10. High megapixels may allow you to cheat with your telephoto shots by cropping in but a lot of factors like pixel density and AA filter will determined if it will be a good shot.
The MMs is only one thing to consider in a lens. I have a 1000mm lens that can do a full frame shot of the moon. It however has low resolution and is very slow at a fixed f 10. That means the shutter has to stay open longer to get enough light meaning that even with image stabilization and a tripod I have to deal with motion blur. To make that lens very fast, say f 2, would make it extremely expensive and so big I would have a hard time carrying it.
I'd rather carry two smaller zooms than a super zoom. The bigger the zoom the harder it is to create it with quality on both ends and they are usually slow. Great for decent shots in the sunny out doors but in a forest or indoors they can be lacking.
The last thing about a long zoom, even a quality one is detail and sharpness is connected to proximity. I can take my high quality 400mm set up or get up pre dawn and find a nice hiding spot or even better a blind and shoot the birds from a few yard or even feet with a 50mm. Those close up shots will blow away the distance shots every time. So zoom with your feet if you can.
The last thing is knowledge. Most point and shoots have a manual mode but rarely are taken off of a automatic setting. That's why they are called point and shoot. Most DSLR's also have auto modes but to get the best out of them you need to understand photography and be able to set the camera settings yourself. Only you actually know what you want, where to focus, etc.
I can't recommend a certain system because there are so many that will do a good job. You need to research, decide how much you can spend and carry, they get to a camera store and see how it feels before you buy. You can research online at a number of sites, I recommend dpreview.com. They have a number of forums not just on the different brands but also specific models. The people there will know the good and bad of the gear, use it and can answer most any question.