Options come down to,

• the server can bundle many images and send them as a single response to a single click
• the browser can simulate multiple requests using a single click
• there is a single click that downloads a single file, that is a bundle (zip file, as mentioned below)

Downloadling multiple files will cause the browser to ask where to place the file if they have it set to do that; if there is a file name conflict, it may or may not get resolved automagically. There are also plugin for bulk downloading, though that doesn't solve the problem that you're displaying the low resolution but want to allow people to download the high res - unless they are smart enough to look at the hyperlinks (e.g., look for ahrefs that end in .jpg), and if that's possible then just having the links somewhere in the HTML source might be sufficient (maybe hyperlink the low res images to them in the main view?).

For you, the idea of selecting which to download using checkboxes, then having the server serve them a custom zip seems to be the most user friendly. But the implementation of this for you is the more complicated (not hard though) of all your options. It'd just require a: form (checkboxes) + handler logic to zip the "selected" files and respond back with a file download of the .zip.