All the pictures at iCloud Photos are also on your iPhone if it's connected to iCloud. If you "Optimize Storage," then the phone will use smaller, screen-sized versions to save space. If you need to edit a picture, Photos may need to go to iCloud Photos to retrieve the original full sized file. Originals of videos, which take up significant space, are often kept in iCloud.
If, as you say, you have plenty of space on your phone, then there is no reason to turn on "Optimize." If you already have for some reason, then many of your original picture files will have been offloaded to iCloud. You can turn "Optimize" off, and when you need an original, it will be pulled from iCloud and will remain in your phone.
Have you turned on "Optimize?" If so, and if you don't want optimized storage, then you should go to Settings>Apps>Photos and change "Optimize iPhone Storage" to "Download and Keep Originals."
You mentioned something about "Select Photos." If you mean that you want to have some originals kept downloaded but others to be kept at iCloud, then that is not an option.