I would strongly suggest renting a car. You are talking close to 55 miles between Sanford Airport and the Beach Club. Taxicab rates are $3.25 for the first mile and then $1.75 per mile thereafter, for a total of about $100 each way (plus tips).
This way if you want to go to the Studios or Animal Kingdom, or one of the other (non-Epcot) resorts or off-site you will have the car available. Depending on the size car, and your length of stay, it might even be less expensive than taxicabs even if it just sits in the parking lot for a few days.
Taking the main exit of Airport Blvd, it will get you on the Greeneway (SR 417) at Exit 50. Head South and go all the way to Exit 6 (marked International Drive). Do not turn onto I-Drive itself at the traffic light, but go straight onto SR-536, World Center Drive. Pass the Marriott and when you cross I-4 you will be on Epcot Center Drive. Take the second exit (marked Epcot Resorts) onto Buena Vista Drive. The follow the signs to the Beach Club.