I am viewing the "images" tab on the page in Showkase and there it shows the pixel dimensions of the photo. I understand that is not necessarily the size it is displaying, but I am guessing the largest size it will show when possible (without pixelating)
If there are multiple different sizes associated with an image, then the dimensions shown on the 'Images' tab are those of the medium images. There may or may not be large and small size images, too, but there will always be a medium image and it is always the medium image whose dimensions are shown. For clarity, the medium image is the image directly inside the corresponding gallery's 'images' folder (i.e. not inside the 'large' or 'small' folders).
Also, when I say there is always a medium image, this is just a label. The medium image could, in theory, be the only image size being used but it could actually be a very large image (in terms of both filesize and resolution) if you want.
Under most circumstances (check the Multi-Size Image support page for details), it will be the medium image which is used for the gallery display and, if there is a corresponding large image, the the large image will be used if the image is opened in a new tab (via the 'Open Image' button), downloaded (via the 'Download' button) or if the gallery is expanded. (If there is no large image, then the medium image will be used for all occasions.)
Whatever image is displayed in the gallery, it will be dynamically scaled (at the time the gallery is displayed) according to the value of the Juiecbox-Pro imageScaleMode configuration option.
A short description of this configuration option and all its possible values can be found in the 'Main Image' section of the Config Options page here.
By default, imageScaleMode is set to SCALE_DOWN whereby images that are too large (in terms of resolution) to fit within the gallery's image area are dynamically scaled down to fit within the gallery's image area whilst respecting the image's aspect ratio and without cropping. Images that are smaller than the gallery's image area are not scaled up (as this would reduce their visual quality). Such images will be displayed at their actual size (perhaps with some space surrounding the images).
You could (if you wanted to), have small images dynamically scaled up to fill the gallery's image area (again whilst respecting the image's aspect ratio and without cropping) by setting imageScaleMode to SCALE (although I would not recommend it for most users).
In looking at the ACQUA demo...
The AcquaPhoto Fashion gallery (for example), is a single image size gallery (there are no large images).
All images in the gallery are 1024 x 640 (except for one which is 1024x648).
In this gallery, imageScaleMode is set to SCALE so, on a large monitor where the gallery's image area is larger than the actual image dimensions, the images are dynamically scaled up to fill more of the gallery's image area than they would if displayed at their actual size. (This accounts for the drop in quality that you see when you expand the gallery on your high resolution monitor.)
It is just a demo gallery but the following changes would be beneficial:
(1) Larger gallery images could be used so that when the gallery is viewed on a high resolution monitor, the images do not need to be scaled up to fill the gallery's image area.
(2) imageScaleMode could be set to SCALE_DOWN to prevent small images from being dynamically scaled up.
(3) Two images sizes (medium and large) could be used so that, when the gallery is expanded, the large images are used instead of the medium images.
With that in mind, please tell me which boxes should remain checked.
I can't really tell you which settings to use. It's a personal decision that only you can make. Different settings are useful for different audiences.
If your target audience is likely to be viewing your galleries on mobile devices, then there's perhaps little point in providing the gallery with large images and setting imageScaleMode to SCALE might actually be useful.
Having said that, it sounds like my three points above referring to the AcquaPhoto Fashion gallery would probably be useful to you, though.
If I will now be needing to upload different size files for each image, will I be better off doing this in a different manner?
If you want to use different image sizes, then it would be best (certainly easiest) to let Showkase resize them for you.
Just make sure your source images are large enough and set your image sizes on the 'Multi-Size Image (Pro)' section.
Showkase will not upscale source images when resizing them during upload. For any given image size (small, medium or large), if an image is already within the maximum dimension bounds ('Max width' x 'Max height'), then the image will just be copied across to the gallery folder without being resized.
I hope these nuggets of information help to put some of the pieces of the puzzle together for you.