By all means YES! An SLR is right for you.
If you want to learn and understand the variables involved in photography, a manual SLR will get you going. By manually playing with focus, aperture and shutter speed, you'll get a first hand feeling of what effect each one has. A Pentax ZX-M comes to mind. Autofocus cameras have come a long way in recent years, and you can get many features for almost the same price of a manual. The Pentax ZX-50 comes to mind. These cameras will do almost everything for you, selecting the parameters, but also allow manual over-ride so you can decide on the parameters yourself.
A huge advantage of interchangeable lenses is just that: you can get an endless amount of lenses from fisheyes (around 9mm focal lenght), to wide angles (28mm) to normal (50mm) to medium telephoto (300mm) to hi-end telephoto lenses over 1000mm in focal lenght. Have you seen a baseball game with photographers in the Center field taking close ups of batters? Those are huge telephoto lenses with big apertures, so they are called "fast" lenses. As a rule of thumb, use the 50-55mm as 1X, so a 300mm is somewhere like a 6X and so on. The most versatile lenses are the zooms like 28-80mm that will give you a range for composition, so you don't have to walk back and forth. And there are many brands out there to fit almost any SLR body.
But remember, the higher-end the camera, not only the more expensive, but the more electronics in it, the more delicate typically, and they use a lot of battery power. Mechanical manual SLRs like the Pentax K1000 use battery only for the light meter, but will always shoot.
I hope this helps.
What makes you think I'm a Pentax guy?
Thanks,
Ismael