Tommy,
Congrats on your new house and land. You definitely have a lot to think about and do if you have never owned a big piece of property. First thing, don't get intimidated by it. This is a long term investment for you and will take you a very long time to learn the property and how to go about maintaining it.
From looking at the arial picture you posted, the property does not look to be overgrown (that is a plus for you). If you came from the city I am assuming you did not have much of a yard if a yard at all to maintain. Just cutting the grass right now every week is going to keep you busy. Depending on how tight your money situation is a tractor might be too much money right now. I think you are going to need a lawnmower, weed eater and chainsaw in that order right off the bat at a minimum. You can make/buy a lawn trailer to pull behind the lawnmower to collect branches and brush around the property.
I also agree with 2ndhalf about getting to know some local farmers and seeing if they might have a use for some of that pasture. If you have neighbors around you that farm or have acreage like you, go introduce yourself to them and tell them about your situation. This is the most important advice I can give to you. Most country folks will be more than happy to help you out and give you advice on maintaining that property. They can be an invaluable asset in your life. They can also help you in tractor purchasing and might have or know someone that has a little tractor you can buy.
When I bought my place I went over to my neighbors house and introduced myself. We have become very good friends and they are farmers. They have helped me fix my tiller, work on my tractor, fed my dogs while I was out of town for work, and anything else I have ever needed assistance with. I can't begin to tell you the knowledge I have acquired from them. (TRULY INVALUABLE). In return me and my wife have them over for dinner and make them a lot of baked goods all the time. We look out for each other. They have also given me some of the best advice about tractors that I have ever needed. I honestly would consider them to be family. My daughter goes over there and sees "Nanny" all the time and gets treats. This will become your BEST support at your new place if you go about it the right way. I really can't stress this enough, make friends with your neighbors and local community. You will be surprised what positive outcomes can originate from doing this.
I know I have not really given you any tractor buying advice. However, from reading your post and the info you provided this is what I would recommend for you to do to get a positive start. You will get overwhelmed at times but hang in there and work hard. You will learn things you thought you would never be able to do. Good luck with your new property.