"keyhole"
With an outdoor gate, rain and damp are the big problems as they will make most locks go rusty.
I have had good results with a Squire 660 padlock, which is a big, old-fashioned looking thing with a galvanised steel case, and the internal levers are brass. It has lasted much better than any padlock with a cylinder (key is shaped like a Yale)
If you want to fit a mortice lock, you need a gate which is quite thick (as least 44mm like a front door). However they all have at least some steel parts inside, as far as I know. A better one like a Chubb mortice lock has mostly brass working parts inside, but the case goes rusty especially round the keyhole. Ordinary cheap 3-lever locks are usually very poorly made and will rust and break quickly. You can buy second-hand Chubbs on ebay, but be sure to get one with plenty of spare keys or new copy keys will cost you more than the lock. Also, fitting a mortice lock requires a fair bit of time and skill if you are not used to chiselling.
There are a few all-brass rimlocks available, as used in Utilities cabins, but they are very expensive. A second-hand Safe lock would be available on ebay, old ones are all-brass and can be mounted on the inside surface of your gate, and have a long key that will go all the way through. You can still get L&F brass safe locks new, and they are not very expensive. However you would not be able to open it from the inside as it only accepts a key from one side.
You can get cheap pressed-steel rimlocks made for sheds and gates, but they are very weak and insecure. It would not hurt to make a plywood cover for such a lock to keep the weather off it.