Physical pictures

Your printer's scanner should be all right as long as it's clean. Scan in the highest resolution available to you. The only reason to scan in anything higher than 300 dpi is to increase the size of the image if you were to use it in a print document, but it's better to get as much data as you can while you're doing the work.

As far as format goes, I would recommend TIFF. While JPEG is common, it is a lossy format, meaning that you will lose data from the file each time you save it. JPEG tosses out data in order to compress the file as much as it can. TIFF is a high-quality format, but that quality comes at a cost in terms of storage — the files are going to be big, especially if you ramp up the resolution.

Storage is a consideration. You should store your files in a system that is backed up regularly, and you will likely need to update your storage media every few years. Hard drives will fail, inevitably. And be sure you keep your original prints in a safe, cool, dry, dark place in case you need to scan them again.

Check your printer/scanner for the dpi setting. 300 to 600 dpi would be best. I'd save them as plain JPGs since they seem to be pretty universal. And make back-up copies of the files.

Cloud storage in 2 locations (i.e. - onedrive, google drive) and two hard storage (flash drive, hard drive etc..)

Depending on the printer you can choose the quality of the scan. You can look up the specs for the printer and see the quality of the scans.

Also you can test it out with one photo.. scan it and print it on photo paper. If you're happy with the quality youre good to go..

Im not too familiar with the best file type.. i have seen large databases use tiff format tho..

What scanner are you using? As another poster suggested, save in TIFF format. Another option is the PNG format. You can get very close to lossless while having some compression to save space. I have a scanner, and it can scan to 1440 dpi I think, but rarely go above 300 dpi as the amount of digital space it takes is very taxing. I do scan at a higher resolution sometimes if I want to edit and restore some parts but then reduce the resolution to 300 dpi after to preserve hard drive space.

Your scanner/printer, if a newer one, should be able to scan a picture quite nicely. Mine is 10yrs old and the picture look great. Make sure the settings are correct - color, 300 DPI or better, lid sits flat and tight ( I used a book), manually set the file name. ( all scanner pictures use a common name). Once scanned, you can use an editing program like photoshop elements to sharpen, repair, etc your pictures.

I once took a smartphone photo of an old photo print (made when I was 18).

It turned out well, as long as I placed my camera exactly above and made sure lighting was clean with no reflections off the glossy finish. Unfortunately it also picks up all the deterioration in the print. But once digitalized, I suppose one could clean things up.

Depends a bit on what quality you want to get as a result. When I digitalized my last pictures of a vacation trip (roughly the same amount as yours), I used a professional service to scan the negatives and got a nice high resolution picture in return.

Depends...
How old is the scanner?
What's the maximum resolution you can scan at
Can you save them as. Png format

You should be able to scan them just fine

I totally agree with @DunningKruger on this