To add some weather protection on your new or existing wood fence you can simply paint it. For best results, use a primer and allow that to dry fully. Then apply an exterior grade paint, I recommend Sherwin-Williams Superpaint, but similar quality will do. This will provide the best protection. Paint every 3-5 years.
Staining your fence will provide less protection than painting it, but it will cost less to apply and will hide imperfections well. It also provides a natural look and can be reapplied throughout the years for a deep stained wood effect. Reapply every 1-2 years for best results, but the original stain will last much longer than that as it fades. MiniWax stain is fine or similar quality.
If you really like the look of natural wood and stained wood, I would recommend putting a finish on your wood to further protect it from weathering. A topcoat polyurethane finish will protect the stained wood underneath from fading. It will also provide a sheen or shimmer that you won’t get with just stained wood. I use ZAR Polyurethane Water-Based finish that can be found at Dixieline. You’ll want to reapply yearly for the first couple applications and after you’ve built up a thin protective layer you’ll be able go more and more years before another coat is necessary.