If your primary target is preparing images for print, I'd say set up one calibration preset with monitor native gamut. The objective of doing this is so that the full range of colours that the monitor can produce will be available to you to see as you edit your images. Monitors that claim a near-Adobe RGB gamut may lead you to believe that Adobe RGB is an appropriate calibration choice, but if you wish to get the full value of the monitor's native performance I'd say this isn't the best choice. That's because the display panel in fact will almost certainly fall short of Adobe RGB is some areas, and actually exceed it in others.
The whole point of colour management in my opinion is to correctly characterize the colour performance of a given device, and allow the full range of colour reproduction potential of that device to be consistently and appropriately realized when moving image data between devices. If you constrain a device to an artificial colour space, that's needlessly leaving part of its performance envelope on the cutting room floor.
sRGB for the web is a special case. If you care about it, you can set up another calibration preset and switch the monitor to it if you want to and use it to review images that you're prepping for the web. Personally I don't do this for several reasons. First, I also target print and frankly don't really care a whole lot what my images look like when they're not in my chosen presentation format. Second, most monitors that claim to be roughly sRGB class devices don't in fact exactly cover sRGB (just as most near-Adobe RGB devices don't excatly cover Adobe RGB). So viewing an image in sRGB is not an accurate representation of how the image will look on a device that isn't in fact an sRGB device. Finally, by far the vast majority of sRGB devices out there will not be calibrated in any sense at all. So using a colour managed workflow to preview images with great accuracy in a simulated sRGB environment, and then throwing them out in a seething sea of colour chaos seems to me like going for 10 decimal digits of precision on a numerical value with error bars +/- 50%. It's just not a worthwhile enough exercise for me to spend any time on it.
In terms of ProPhoto RGB, I'd say there's no point attempting to calibrate a monitor to this colour space even if software would let you attempt it. (And I'd be surprised if it would let you make that attempt, but I'm not familiar with Eizo's calibration software.) That's because ProPhoto RGB is so drastically beyond the gamut of any monitor that I's say it's pretty useless to attempt to characterize the colour reproduction of a monitor with reference to ProPhoto RGB. Using monitor native gamut should give you the maximum colour reproduction range the monitor is capable of... there's no reason I can think of to try using a wildly over-shot synthetic colour space as a reference for the monitor calibration run.
Where ProPhoto RGB makes sense is as a working space with your editing software, because it's large enough to contain image data that must be shipped amongst a range of devices (cameras, scanners, monitors, printers, etc.) that have a very large variation in colour gamuts. These gamuts are non-overlapping with each other in a lot of areas of the colour range, and they also can exceed Adobe RGB in a number of relevant areas of the gamut. (Of course this is dependent on the subject matter you photograph, and the actual colours found in the images you capture, edit and print.)
You do have to be more careful with your editing when using ProPhoto RGB, since it exceeds what your monitor is capable of displaying and therefore you may unintentionally push the image colour in ways that "cook" it without realizing that's what you've done. For this reason, a lot of folks choose Adobe RGB as their default, go-to working colour space. Adobe RGB is a relatively close to many modern monitors' native gamuts, and it covers a very large range of real-world colours that you want to carry from capture to print. But there are real-world colours that you can carry from capture to print that fall outside Adobe RGB, so for those there is ProPhoto RGB.
Side note: colour spaces like sRGB, Adobe RGB and ProPhoto RGB are synthetic colour spaces. They are artificially created for purposes primarily to do with processing in various intermediate stages of imaging workflow. Camera profiles, monitor profiles, scanner profiles and printer profiles all contain device-specific colour spaces. They are created primarily to characterize the specific colour reproduction of an actual device (or at least a class of very similar devices that can be expected to behave very much like each other). Device-specific colour spaces have the primary purposes of allowing the imaging workflow to render image data into or out of the device in a consistent & appropriate way. Mixing up the purpose & use of synthetic and device-specific colour spaces is rarely something you'd want to do on purpose. In some cases, the negative consequences can be fairly minimal, e.g. calibrating a near-Adobe RGB monitor to Adobe RGB instead of the monitor native gamut; still, in most cases I'd say there's no upside to using a synthetic colour space to constrain the colour reproduction range of an actual device, when calibrating that device.
That's my take on it...