Hello mate,
I use 13" coil from 2 years and im going to hit 1000 coins for those years. Dont think that Ive been on places that there no one have been before. Before me there have been people from 20 years ago. Here in my country treasure hunting and metaldetecting is more profession then a hobby, hehe.
13" is the deepest coil from all of the rest. My personal tests that I have done prove it and there are some nice test that you can see in YT:
11" - https://www.youtube.com/watch?v=_YE88FXXuBw
13" - https://www.youtube.com/watch?v=7rBg0Jmtjgc
Why is the deepest - because it is the largest

But here is a catch. As larger is the coil as better will perform for larger items in a greater depth, but worse will be for smaller items. I found that for coins from 18+ mm. and up, 13" is the best choice.
You will say - Yes, but there is a extraordinary items smaller then 18 mm.
True, but not many. More interesting things are deeper and they are larger like - As, dupondius, sestertius, medallions (all 28+ mm), figures (10 cm+;especially they are very deep buried, 40-50+ cm. deep). End on last place, but not by priority; 2-3 up to thousands coins gathered together - a Hoard! Isnt that all we searching about

So if you use smaller coil, the chance to miss all of the above is greater. I mean to miss them when they are buried in a greater depth. Dont count that you are first on the site and no one know it and never been there before. Probably someone already detected largest, swallow and easier to detect items. The point is hit the Tartarus! Search deep.
About HF coil.
As higher the frequency as smaller items you will be able to hear, better will penetrate the soil (especially if it is rocky like ruined castles, ceramics (as roof tiles) and mineralized ground) because soil is a kind of dielectric for the radio waves, but here is the catch

Your depth will be smaller.
As lower the frequency, deeper you will penetrate, larger items will be able to detect, but wont be able to discriminate well and will hear closer to iron sound (ofc when they are on the frontier). Here is how I use kHz ranked by popularity;
7,7 - fields (especially good when it is ploughland), meadows.
11,5 - when fields and meadows are more rocky or passing above houses (easily you can notice it by higher mineralization on that spot) or very dry lands.
17,4 - highly mineralized ground, rocky places, roads, ruined castles etc.
4,0 - checking for everything in descent depth.
Here is one video that will give you an overall picture. Nevertheless is about GPRs, principles are same;
https://youtu.be/oQaRfA7yJ0g?t=44
Personally I would not use HF coil for coin and relic shooting, unless I want to suck out every coin that is laying on the edge from the upper layers. I would use it for a second run or in conditions that I listed above. It is a coil more suitable for a gold and beach hunting.
Shortly, 13" (on first place) and HF 9″ round coil is your choice
Ahh yes btw, 13" is a heavy coil so find some a self-contained belt (dont know exactly english name Minelab got nice gear, called "Pro swing - 45"). I advise you to use it even with lighter detectors. It will safe you energy, prolong you hunting day and most important will keep your shoulders healthy.
And remember - best discriminator is you shovel !
Sorry for not perfectly used English grammer and Happy hunting