Suealpha wrote: …Is my Mac geared up to help me get all my photos into the app designed for them without too much difficulty?
Well, sure-- it may depend on what you mean by "too much difficulty."
The following information may get you started:
While Finder is a File manager, Photos is an Image Manager, and so you get a concentration on things unique to images, like the date it was captured, the camera that was used the location where it was taken, the people in the picture, etc.
If you have a "Family" folder full of old pictures of the family, then you can drag the folder to Photos and you'll see a screen like this:

Then the pictures will all be put into an "album" and named Family. If you have a folder of folders of pictures, you will get a folder of albums of pictures.
Vocabulary:
- Pictures are imported to the Library.
- Pictures and data are kept in the Photos Library package in your Pictures folder. They still exist where they came from, and these originals can be kept as backups, perhaps on an external drive.
- Pictures can be put into Albums.
- Albums can be put into Folders.
A folder can contain other folders, but not have pictures.
- Photos is a non-destructive editor. This means that original picture files are kept untouched inside the Library package. When you edit a picture, remove spots or whatever, Photos remembers the steps you took, and it re-applies those when you need to see or export the edited picture.
- Smart Albums can hold pictures based on criteria that you choose. You can make a Smart Album with all the pictures taken with a Nikon E2600 camera between 1/1/1999 and 7/4/2005, for instance.
- Keywords can be applied to each picture to make them easier to organize and to find.
- A picture can be give a short Title that can appear beneath thumbnail images
- You can enter a Caption for each picture to give a fuller description.
- iCloud may be used to synchronize the Photos Libraries on different devices.
- Unfortunately, so far, Titles, and Keywords don't appear on iPhones, though they can be searched for. Captions appear on both Macs and iPhones.
About your two places at once question:
In Photos, pictures aren't exactly "in" an album. When you "put a picture into an album," its name is added to a list of pictures from the Library that display together when the album is clicked, kind of like a music playlist, but for pictures. So two albums can both have the same picture name in their lists (like two playlists with the same song,) and that picture will show up when you click either album, but there's only one picture file-- it's just on multiple lists. And when you remove a picture from an album, its name remains in the lists of other albums, and the file still remains in your Library. You don't get fewer pictures in your Library because you remove one from an album; you just get fewer names in the album list.
So albums give a specific view of your pictures. The picture of "Aunt Ethel at the Grand Canyon" can be in the "Aunt Ethel" album with other pictures of Aunt Ethel, and it can also be in the "Grand Canyon" album with pictures of other people at the Grand Canyon. And it can also be in a the "September 2015" album with other things that happened then. Each album is pointing to a single file stored in the Photos Library, so having pictures in multiple albums takes up no more storage space. As you can imagine, this is very powerful in organizing pictures.
There are special views provided by Apple. The Library View is provided by Apple to give a view of all of the pictures in the entire Library in the order of their "taken" dates or their "added" dates depending on a your menu choice. There are a number of automatically generated smart album like things that you have no control over.
Feel free to keep asking!
You could see this
Photos User Guide for Mac - Apple Support