There are a number of factors that will contribute to how well the salt penetrates the interior of the piece of fish including thickness of the fish, types of tissue that have to be penetrated, and length of brine. The skin creates a significant barrier to salt penetration and the solution will penetrate the meat from its face and from its leaner side. After brining there will be more salt near the lean face than near the skin area. In order to get the most even salt penetration remove the skin, cut the pieces thin like sushi or ceviche, and brine in a 15% salt solution for 2-3 hours. For even penetration you need even contact on both sides of the meat so you either need to suspend the pieces in the solution, or flip them at regular intervals.
The surface will always be saltier than the core, but with thinner pieces and sufficient time the difference will be negligible.
If you want to use larger pieces you will need to extend the time. Consider combining a soaking brine with injections of the brine solution into the meat itself.
You could brine any kind of fish that you would find in a sushi restaurant, just make sure it is as fresh as possible.
After reading citizens comment I was able to find this site which states that salted herring typically has a salt concentration of 7-13%, however this article's abstract leads me to believe that a dry cure then brine combination may be responsible for the higher salt concentration. According an article about hams and sausages, wet curing methods can reach salt concentrations up to 26%, but maximum weight gain is reached with a salt concentration around 5%. The first site also notes that salt concentrations above 7% are considered unpalatable by most people.