Most of the lightbox type plugins are simply to do with the way images display, ( as opposed to next gen which is a gallery plugin used for managing galleries and albums). Usually with lightbox/thickbox plugins you just install them and if you like you can adjust the settings but that’s all there is to it; when you click on an image which is linked to itself ( by default they are ) then they open up in lightbox ( highlighted floating image) etc rather than an attachment page.
NextGen is a serious piece of kit and you will need to spend a fair bit of time playing with it to get it to work for you, including reading docs and looking for tutorial type videos and posts to get it working. It is worth it though as it’s a quite good gallery system ( if you only need a simple gallery then research the built in wordpress gallery which is fine for small galleries and much easier to use). It will take a good bit of work to get working though and there are a few different places the whole thing can fall apart if you’re not familiar with it. All the same if you have a gallery or album which you can view in the galleries section then you should be able to display that gallery using one of the shortcodes. Try putting the shortcode into the HTML editor as opposed to the visual one and then saving before going back to visual. Another possible solution would be to try a new page for the shortcode, sometimes they get a bit mixed up. Also dont mix up galleries and albums. If your shortcode is for displaying an album then you’ll need to add galleries to that album first.