The best coils for Prospecting are the High Frequency (18.75kHz) coils.
Since you also like to hunt for relics (I assume), the same coils will serve you well on both beaches and elsewhere.
The higher Frequency is better for mineralized soils such as where Gold is usually associated. These soils interfere with the signal from lower frequency coils. Likewise, salt water can create a conductive saline event which again is better served with higher frequency coils.
Note that the 6" DD HF coil and the Elliptical DD Coil are both designed for use on Goldfields. However, the Elliptical is best for scanning large areas and exploring whereas the 6" is a little more specialized and is better suited to exploring smaller areas and use in creeks etc (the 6" is waterproof but the Elliptical is only water resistant).
The 6" is superb for trashy areas like old homesteads etc. It's extremely sensitive and punches deeper than the Elliptical. However, it has to be used a little more slowly and therefore is not as good for exploring larger areas.
I'm just editing a short video together now which briefly describes the differences between the two with some animations ... should have it finished within a week (there's other material I need to work on). Will upload to YouTube when it's done.
The illustration below shows how different they are side by side: The larger Elliptical Coil will ignore smaller pieces of gold but has a larger Secondary field with a shallower blade. It will react to anything over a certain size within both primary and secondary fields. The smaller 6" coil punches deeper but will miss almost anything that the blade does not touch. Hence it's extremely sensitive and perfect for high trash areas yet unsuitable for larger areas because you have to move slower with it than the Elliptical.
Cheers,
Marco