What's the best, cheapest, safest fencing?!
That depends. Each person has their own preference for best or safest. For small dry lot spaces I would use board fencing or no climb fencing, reinforced with a top and bottom board. For pasture fencing, electric wire or rope is inexpensive and works well IF properly installed and maintained. Use quality posts, fasteners and charger and make sure your ends and corners are properly braced. Cheap fencing can be very expensive if it doesn't contain or injures your horses.
As an example, I have two 3+ acre paddocks fenced with 3/8" electric rope (4 strands) hung on treated 5-6" treated wooden posts, spaced 16-20' apart. We electrify the top and third strand and use screw in insulators. The posts are 6+' long pounded 2' into the ground. I also keep the grass trimmed under the fence and mowed just outside the fence to discourage the horses from reaching through. For the past 4 years (and counting), this fence has been safe, inexpensive and easy to maintain.
With 4 horses on about 7 acres, I have to manage my pastures carefully. We pick up manure at least once a week in spring and spread / harrow a couple times a week in summer. I watch the manure load and weeds carefully to decide whether to pick up and pile manure or harrow. I use inexpensive plastic step in posts to cross fence and rotate my grazing areas. One or two strands of electric is fine for this, but the perimeter fence is much more secure. If the grass gets short and needs a rest, I either assign a sacrifice area or arrange to pasture the horses elsewhere for a few weeks at a time. We have productive summers but cold, long winters so I feed hay from about Oct 1 to the end of May. You can count on feeding at least 100-150 60lb square bales per horse per year in this time.
With less space, you will have less grazing and so will need good fencing and more hay. A dry lot paddock with shelter and water would be a first priority. Also make use you have some place and means to handle manure. Some people rent a dumpster that is dumped every couple of weeks, while others compost a pile or arrange to give it to a local farmer or mushroom farm.
Keeping horses at home is no small task and requires a huge commitment to the horses, the fencing, and maintenance of the property. I wish you the best in this new adventure!