Thank you, didn't know it was called "DAM". I am used to Windows... and finally made the move to MacOS.
How is it getting managed by the software? It might sound weird but not having "total" control of my photos, I am afraid I can lose them.
You will not lose them. With most DAMs, the originals will never be touched or modified... even if you make changes. I'll discuss Aperture 3 (A3)... since I use it the most.
You have two choices where to keep your originals... either in the library itself, or in any folder structure you choose. For a small library like yours, I would generally suggest "managed originals"... in the library. However... the library is really a "package" that you can go into... and your originals will always be sitting there... just like any other folders.
The power of a DAM is incredible. I'll suggest that you read some very inexpensive ebooks by a Mac Forum regular named Robert Boyer... his site is photo.rwboyer.com and his ebooks are worth their weight in gold. Get A3 Organization and A3 File Management.
To give an example of what you can do... I'll give an example.
When you import your originals... they go into what is called a "project". Each original lives in one, and exactly one project. From there you have a lot of options on how you classify your images. Generally, I'll assign a location to each project, unless I am using a camera with a built in GPS (as an iPhone). Within seconds you and flip through your imports, accepting/rejecting photos... and rating them from 1-5 stars. You can assign keywords on anything that is important to you... and on and on.
Although photos live in only one project... they can also live in as many albums as you choose. The wonderful thing is that they do not take up any space... photos in albums are not duplicates. You can populate the albums by using any criteria you choose.
Then come smart albums. You can create these and they will auto populate with any criteria you specify... and as you add new photos... the smart albums self configure.
So... you decide you want a slideshow of your best beach vacations. You create a smart album that contains all pictures taken on the Oregon coast or Hawaii, with at least one of your children, but not the dog, with ratings 3 stars or above. As quickly as you can open the album... it is populated by all photos that meet that requirement. Seconds later, just those pictures are playing in an slideshow on your computer, or on your Apple TV.
Your daughter is getting married... you create a smart album of just her growing up rated 4 stars or above. You quickly go through those and print the top 50 for a photo collage to have at the reception.
You get the point. A DAM opens this capability for you.
Any good DAM will do these things. I personally think that iPhoto is too limiting, but it is already on your computer and it is free. It integrates wonderfully with your Mac... and your photos can easily be referenced from lots of other applications... or synced to your iPhone.
Aperture is a "grown-up" version of iPhoto. I love Aperture, and think the program all by itself is reason enough to switch from a PC to a Mac (Aperture is Mac only).
The other great DAM is Lightroom by Adobe. Like Aperture, it is quite powerful. You will get strong proponents of both A3 and LR4. Both are good. I love that Aperture integrates with a Mac so much better... and Aperture's workflow is arguably the best in existence.
Enjoy...
/Jim