Initially Earth was very close to a water world.
From about 4 billion to 2.5 billion years ago The early Earth was a lot more tectonically active than today, due to the combination of the energies of accretion, radioactive decay, and the formation of the metallic core. It was during this time that the Earth's crust cooled enough to be called solid, although again, there was quite a bit of tectonic activity.
This activity generated structures called cratons, which are the oldest rocks on earth, about 5-7% of the total crust. Cratons are like daggers of rock that reach deep into the mantle. The Canadian Shield is one example. These structures are also the place where diamonds can form, deep enough for the pressure to create them, and then they work their way up to us in a few places, such as the Kaapvaal Craton in South Africa.
Even at this stage there was evidence for deep oceans on Earth. Volcanic eruptions under water generate distinctive shapes known as pillow lavas. More to the point, these oceans had sky high iron content, not surprisingly. What they also had was some kind of photosynthesizing cyanobacteria, which is how the distinctive banded iron formations are created.
Now, there is a trick one can do, given tectonic activity, and moving plates. The plates will move around the planet, dragging the cratons with them. Cratons, for all their durability, are a fair bit lighter than the basalts that are erupted under the sea to create the sea floor. These eruptions happen along the fault lines that make up the oceanic ridges, pushing basalts outward.
As these basalts cool, they become denser and eventually slide under the cratonic plates, and sink towards the mantle, along with seawater, which makes the rock thinner.
These are the subduction zones. Alaska, California, Japan, Indonesia, the Andes, the Rockies, the Ring of Fire is where this process happens.
This thinner rock is heated and forced up to the surface. Some of it is molten, and gets erupted into igneous crust, like we see in Scotland, and the Black Mountains in England, when it passes over a hot spot, or mantle plume. Compared to the plates, this rock and water mix is frothy, and light.
This process is how continental crust is created, more or less, over geologic time. Fresh rock from the oceanic ridges, pushed outwards, cooling as it goes, until it is heavy enough to sink back to the mantle, except that the water makes the rock thin enough to be erupted via surface vulcanism, the lava flows become new land. This new land gets smashed into other new land at the subduction zones, or pulled apart which allows for more vulcanism, and more new land.
Now, Earth possibly went through something called the Late Heavy Bombardment which would have brought a great deal of water bound in the rocks themselves. However, your planet may not have gone through this. YMMV.
Over time the continents will become bigger and bigger, and drift will eventually create a super Pangea type continent.
This structure will last for millions of years. There will be heavy rainfall near the shores, and a vast, world sized desert in the rain shadow created by the uplifting of the crust to create the continent. The salts you require will be all over the interior of the continent, which will be vast, but most of it would have been sea floor a few million years ago. There'll be your salt, as well as limestone, everything you might want, but almost no water.
The oceans and coasts will generate enough oxygen to create an ozone layer, so your desert can be utterly dry, like the Atacama, or the Gobi, and yet not sleeted with killing UV so life can exist.
I think that covers most of the requirements?
