If you’re going to use solar then plan on grounding rods IAW the manual directions. A proper rod will be of a galvanized steel and be 6’ long or so. If your ground is wet year round (ensuring a good electrical ground) then one driven 5’ down will do the job. If you’re in a very dry area then you might need up to three and would be wise to “water” them periodically to preserve their effect.
If you can use a plug-in charger then you might get away with the “bi-polar” wire. I’ve never used it and don’t know what it’s requirements are.
As Alagirl notes wet ground works much better than dry ground, in that the critter being “shocked” is well grounded if the soil is damp (or even wet).
For what you have described, a basic shopping list could be:
(1) Solar charger like this http://www.zarebasystems.com/store/electric-fence-chargers/esp3m-z Zareba is good brand and should do 300’ without difficulty. Note the type of fence post you’ll be using for mounting and obtain proper hardware if not included in the box.
(2) Grounding rods per the charger manual. When setting grounding rods put them in an “out of the way” location where they will not be tripping hazard for horses or people.
(3) Clamp(s) to attach grounding wire(s) from charger to rod.
(4) Fence wire, rope, or tape. All generally excite some sort of “safety” discussion revolving around equine injuries. Any time you restrain a horse it has the chance to injure itself. Aluminum wire is soft and breaks easily; that’s Good News and Bad News. From what you describe it might work well as you don’t have much to run. It’s easy to work with and delivers a good charge. It’s pretty much impervious to weather.
(5) Insulators appropriate in number and type. The type of fence material, post, and placement on the post will determine the type of insulator you buy. Count your fence posts and act accordingly. Get appropriate insulators for the corners. If you’re setting insulators on wood posts you’ll need screws. They are much easier to use than nails.
(6) From the OP it does not seem you’ll need a “gate.” Unless, of course, the horse leaning on the gate is a problem. In that case buy a standard gate handle. When you get to the last insulator “finish” the fence. Then make a gate by cutting an appropriate length of fence material. Attach it permanently at one end and make a “loop” on the other to receive the “hook” on the end of the handle. One thing you can do is hook the “fixed” end of the gate to it’s own insulator, but do not electrify the gate from the fence. Instead, at the “hook” end wire your loop into the “hot” fence. This means that when you open the gate that wire is “cold” and your risk of shocking yourself or the horse is reduced. You also don’t have a hot ware laying on the ground going “snap…snap…snap…”. That will bother some horses.
The tools you’ll need are likely a set of fence pliers (not absolutely necessary but very convenient and long lasting). Drill, auger bit (to make holes), and driver bit (to set screws) if the posts are wood. Battery powered drill is best but you can haul a generator and regular drill if you want to!
Wrench and/or pliers to attach grounding clamp(s) to grounding rod(s). A “driver” to set the grounding rod. A post driver will do; the “hard way” is to use a sledge hammer.
This should do you for a basic list. It looks daunting but is really pretty simple. Fence building is not “rocket science”!!! 
Good luck in your project.
G.