I choose to store the files locally on my hard drive
You can certainly use these images to create a gallery on your computer but you will need to upload the gallery's own images (inside the 'images' folder) to your web server in order for them to be publicly accessible.
The pics are large will juice box resize them?
Yes. As long as the 'Resize Images' checkbox is selected on the 'Images' tab, JuiceboxBuilder-Lite will resize your images.
You can click the 'Change Sizes...' button to set dimensions for the images but the default values will likely be OK.
For the index page name it gives me index.html
The gallery's index page is required only if you want to display the gallery on its own web page and you can call the page whatever you like, it does not need to be named 'index.html'.
If you want to embed a gallery in an existing web page alongside other content, then you should use the embedding code and follow the embedding instructions here.
I've taken a look at the code on your http://www.foxsdengolfcourse.com/Pictures.html web page and if you want your gallery to appear on that page, then you would need to upload the contents of your gallery folder (not the folder itself) to the root directory of your web space. (Do not upload the gallery's 'index.html' file, though. It is not required and will overwrite your own 'index.html' file.)
Alternatively, try the following (using the baseUrl method of embedding which allows you to keep all your gallery files inside the gallery folder).
(1) Create an empty folder on your desktop and name it 'gallery'.
(2) Create a gallery with JuiceboxBuilder-Lite and save the gallery in the folder you created in Step #1.
(3) Upload the entire gallery folder (not just the contents) to the root directory of your web server (directly into your 'public_html' directory) using an FTP program such as Filezilla.
(4) On your 'Pictures.html' web page, use the following embedding code:
<!--START JUICEBOX EMBED-->
<script src="/gallery/jbcore/juicebox.js"></script>
<script>
new juicebox({
baseUrl: '/gallery/',
containerId: 'juicebox-container',
galleryWidth: '100%',
galleryHeight: '600',
backgroundColor: 'rgba(0,0,0,0)'
});
</script>
<div id="juicebox-container"></div>
<!--END JUICEBOX EMBED-->