Need Help With Tv

Please help. So new to this! Really want a new 3124 kb but need to know if I can pull it or if it will pull me. We live in louisiana and would be traveling to FL, AL, Etc. No mountain traveling for now. I have a 2006 Ody but have a friend who is selling a Ford E150 6Cyl van. It has a towing limit of 5000. I called the TM factory to get the weight of the options I wanted and they came to 207 pounds. I added that to 3100 for the TM, 70 for propane and battery, 160 for full tank of fresh h2o, 500 for the family. It all added up to 4037 pounds. I figured 240 for a full tank of gas and 500 for stuff that we would pack...4777. If I ensured a class 3 hitch, weight distributing hitch, transmission cooler would i be ok. We would mostly be using sites that had hook ups. Any help would be great as I have confused myself with reading and researching for hours. Thanks in advance. Tori