A small DSLR will do all you ask and more.
The four thirds system, no matter how loud people shout about it, is dead. It just doesn't know it yet.
The ONLY camera systems worth investing in are Canon & Nikon DSLR - the Microsoft and Apple of the camera world.
Anything else is like buying a Dragon 32 or an Atari - a massive waste of money & time.
You need an optical viewfinder. Anyone who says otherwise is just deluded - you can't take decent pictures if you can't see the subject.
But the most important thing is the manual - a camera is just a box with a hole in it. You need to strip away all the crap and learn how it works.
This takes about five minutes.
If you can tie your shoelaces, you can work it out.
If you just want to take better, as opposed to different, photos, buy a good book, read the manual and learn simple relationship between apeture, shutter speed and sensor/film speed.