Good points rtparty. I shoot with a Nikon D7100 after having gone through 3 other previous Nikons in the 3xxx and 5xxx series. I shoot mostly landscape but will be tuning for aquarium soon

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One of the most important points of any DSLR IMO is to actually learn to shoot your camera in ANY other mode but Automatic! The reasons for this are plenty but the most important is being able to understand what your camera is doing and why. This enables you to tune in on whats the best settings for certain picture types. There's no harm in starting off in Auto Mode if you're an absolute beginner but there's also no more satisfaction than knowing that YOU took your best picture possible when YOU are in control of the camera. Leaving the camera in Auto Mode makes you a slave to it's settings, most work pretty well, where as different conditions can make it impossible to get a quality picture in the Auto setting.
Whatever type or brand of camera you decide on according to your budget and needs is up to you. But please by all means learn how to get out of Auto Mode as quickly as possible. You'll curse me now but thank me later

! I promise. It doesn't hurt to look at your settings and write them down in Auto Mode either, it helps you to begin to understand some important things early on.
At first it's going to be plenty confusing learning the triangle (which you'll understand later) and then add in different lenses and types. The list of components rtparty listed above are what I would definitely consider "absolute essentials"! One thing I would add though is also a good lens cleaning cloth on hand at ALL times! And also learn to shoot in RAW mode as he said and get out of .jpg when you can. The file size is bigger but there is no degredation in the data, there is some loss in .jpg over time.
There are a lot of "how to" books and "Dummies" versions but to be honest there is only one book I've ever recommended to help people get out of auto mode and control their own cameras. If the OPS want to remove this post it's fine, I'm not trying to sell a book as much as help people in what I know works for most. I have no affiliation to this person in any way. This book was recommended to me and was the best and easiest to understand in the quickest manner.
~BEYOND AUTO MODE A Guide To Taking Control of Your Photography by Jennifer Bebb~
I highly recommend Chapters 1-4 and then whatever interests you.