I would start with a 243, 7mm-08 or maybe the 308 if you plan to stick with hunting and ever need the rifle to do more for you. But a 243 is fine for deer. No issues with it at all. A 7mm-08 or 308 will have more recoil however and for a first rig it can be a little unpleasant.
Now personally i have 308 that is far less recoil than my 7mm-08 so keep in mind the rifle design and weight matters. I also have a few 30.06 rifles but since i hunt mostly deer its really not needed and to have more recoil and blast its just not worth it to me.
Burris Fulfield II scope and you are good to go. I would look at Marlin or savage rifles. Both are good for the price. Also the Ruger American. These are budget rifles that do well and will last a long long time.