One or the other... and once you use one, generally you should stick with it. Oil and water doesn't mix and it messes up the cutting properties of the stone when we mix for honing (though that can be fixed somewhat with a dressing stone). A splash here and there to rinse or wash is okay though.
There are pros and cons with using water or oil but they relate more to field use/availability and climate considerations... In a shop or home. It really doesn't matter. The role of water or oil is to provide a little lubrication while also carrying off any swarf on the surface. Using a stone dry will clog it up very quickly and marr performance (again, can be fixed with a dressing stone).
Silicone Carbide, Aluminium Oxide and Arkansas stones can be used with oil. Waterstones should only be used with water. There are synthetic waterstones and natural ones (which can be super expensive especially Japanese Naturals). Enthusiasts will pay the price for a JNat because they covet a certain feedback and edge refinement that can only be achieved with it.
You can also consider diamond plates but those can also be costly as you'd want to buy the ones with electroplated/embedded particles rather than cheap ones with glued on particles - those come off very quickly.
As for your knives, it all depends on the knives you are using and what level of edge you want to put on it. Good stones can cost more than a knife so it's up to you how you value your knives. And if we are serious about sharpening we typically need a small collection of stone grits to work through. Typically 400 or 600 to fix a really dull or damaged edge. 1000 to put on an edge and further grits to refine and polish. 3000 is a general good enough level of refinement for most uses. Most people get a combination 1000 with 3000 or 4000 stone and stop there. And that's good enough TBH.
If you want to go further - 4000 gets you a milky mirror finish, 6000 onwards takes you into a mirror shine... How far to go depends on the cutting characteristic you want. Most knives I take to 3000 for toothiness, a few (my Japanese knives) I take to 8000 for push-cut sharpness.
If you are not ready to build a stone collection, a simple way to get a great edge after any stone is to use a leather strop loaded with a compound. The strop will refine and polish the edge. If I feel lazy or rushed to get an edge I just strop after 1000 rather than take it through the stone grits. I strop all my wood working cutting tools. Stropping regularly also prolongs the interval between sharpening cycles. You can easily make your own strop with a piece of leather mounted on a piece of wood.
Enjoy... be warned though... it's a rabbithole!
