Just my 2 cents on rifles...
Start off test firing with a smaller caliber say a .22 a .223 or a .243 and fire it to get used to noise, recoil, etc. See how it feels...reason being when I started hunting at 12 I developed a flinch when I fired a high powered rifle because I was shooting a 30-06, the recoil was a bit much for me at the time because I weighed all of 100 lbs wet! It took me probably 4 - 5 years to get out of that nasty habit and I eventually settled on a .270. I have fired a .243, 30-30, a .270, a 30-06, a 300 mag, and a .308. Each one does the exact same thing (kills a deer), but subtle differences with each gun can make a difference in your shot.
I haven't really any experience with slug guns, but I'd start with like a 20 guage and work my way down to a 12 guage, again for the same reasons above.
After you have test fired some guns and you've chose your rifle, become comfortable with it by shooting, cleaning, and becoming familiar with the gun's safety, scope, etc. They say treat every gun as if it's loaded...I treat a gun as if it's loaded and a child! You can never be too safe.
As far as getting started...
1. Education, Reading, and Conversing
2. Purchasing Equipment
3. Set Expectations
4. Start getting into the woods
5. Harvest your first deer
6. Advanced stuff...
Everyone has expectations of what they want to get out of hunting. First and foremost I would say the most important part of hunting is just the passion and love of nature and being in the woods. Without that it would be mundane and boring (though text messaging and smart phones have helped with that!)
1. Education, Reading, and Conversing:
As others have stated, go to a hunter's safety course and/or seminars (a lot of gun shows have informational presentations put on by people who are passionate about hunting). Try to read as much as you can to gain a general understanding of what life in the woods is like and what to expect. Like others have stated, tree stand hunting vs. ladder stands vs. ground blinds vs. sitting under a tree vs. walking and stalking! Gauge the experiences of others and what you've read to set your own goals for yourself in an upcoming season. (Take the "trophy shows" with a grain of salt because they are best case scenario and instead talk to other hunters in your area to figure out your realistic expectations from deer sightings to herd size and the works). From there only you can only take it to the next level via practical experience and conversing with others...like on this forum!
2. Purchasing Equipment
Unless you have a TON of money to throw around (couple grand), I wouldn't go out and purchase top of the line hunting gear. See if you can find a local store that sells gently used hunting clothing or an outlet store because it can get VERY costly. If you've never been hunting you don't really know where you'll be 2 years or 5 years down the road and may find you don't enjoy it as much as you thought you would (though I hope you do!).
3. Setting Expectations
From the knowledge you gained via books, conversation, seminars, etc. You will begin to take into consideration how you'd like to hunt and set expectations. This doesn't necessarily mean shoot a deer on by the 3rd day in the woods because that's a whole other learning experience in itself. What I mean is...seeing a deer...how you'll react and how you think you'll respond, move, prepare for it coming into shooting range...How you are planning on hunting ground vs. tree vs. blind vs. walking. If you choose to go up in the air, again, try to find someone who may have a stand and get up into it a time or two and see how you feel sitting on a piece of metal attached to a pole. I love hang-on stands but now I almost prefer a ladder stand or ground blind. I just don't like climbing trees and am a bit skiddish of heights! Remember, just because you picked one doesn't mean you have to settle on it! Try all types of hunting and you'll figure out what appeals to you the most.
4. Getting in the woods
You said you have land to hunt already...after the season is over for whitetail in your area (get the information online or in your hunting book) go into the woods and explore for signs of deer whether it's droppings, rubs, scrapes, trails, antler sheds, etc. If you can get a topographical map or use google earth to assist you with the exact layout you can find starting points as to where to search for deer accessing your land. You will have ideas of where to walk/search based on the information you'll gain from basic hunting books and knowledge you obtain from others via questions. You can also post pictures on here or drawings if you're artistic and ask for suggestions of where to look on your given lot. There are so many knowledgeable people in this forum. Hunting is a 365 day a year sport so just because it isn't hunting season doesn't mean you shouldn't be scouting the woods, fields, and taking walks looking for antlers. The more information you get, the greater chance at success you will have.
5. Harvest your first deer
OK, this is a LOT harder than just walking into the woods, grunting, and a deer running into your stand, boom it's dead. This will probably be the most frustrating part when you get to the actual season. However the adrenaline rush when you see your first deer in stand, see your first buck, spook a deer that is within 15 yards, the thrill of a shot on target is what every hunter lives for! Patience and persistence will get you that first deer and when you reflect on what you did to get there is the icing on the cake.
6. Advanced tactics...
This is what the forum is for...after you have a grasp on the basics of hunting whitetail (it's not just sit in a field or tree and wait) you can begin to explore ways to improve your chances of harvesting deer, improving habitat, using scouting cameras, etc.
I hope, while long, this helps you in the direction you want to go...into the woods!