800 feet is doable as there have been commonly available radio equipment that is actually inexpensive (around $100) that is rated to nearly 2000 feet (we did have radios that were rated to 21 Miles) … this would be an add on to the standard radios (if a radio is included with the operator)
Solar, if the property is your residence, should qualify for the 30% Federal tax credit for the gate operator, its related equipment and its installation—does not include the gate itself or the gate’s installation
If the gate is being used to contain livestock I would suggest installing a slide gate rather than a swing gate and make the slide gate several feet longer than the opening to insure the gate can not be pushed open (make latch side just two posts having the gate slide in between the posts rather than dead end into a latch). If a slide gate operator is to be used build a mounting stand that has the operator at about mid height of the gate primarily to get it off the ground (in the south fire ants can and will eat it apart) The gate speed would be faster for a 12 foot slide verses a 12 foot swing, the slide would be about 12 seconds where as the swing would be between 15 to 24 seconds depending upon the manufacturer
Depending on the location the batteries should be the largest you can get, most DC operators if that come with factory supplied batteries the batteries will be small 7Amph types that were never intended to be exposed to the temperature changes of the outdoors, those batteries were intended for security panel back up power intended to be installed in a climate control room.
Either GTO or Ghost would be equals, both were designed to be marketed as low cost operators. (If you go GTO, I see that Tractor System has the option of purchasing a secondary extended warranty that if reasonably priced would be a very worthwhile investment as often the failure rates for either is higher than most other more expensive systems)
There are many manufacturers available, several will sell manufacturer direct