Saving file as PSD or TIFF or maybe something else?

What you're seeing is the native real size of the file.

What's usually the problem here is that people are used to jpeg, which uses very aggressive, destructive and non-reversible compression to reduce size. Jpeg compression can usually shrink a file down to an astonishing 2-5% (!) of native size.

But there's a price, and that price is so steep that you should never use jpeg as a working format. The file will degrade with every save.

For archival purposes, PSD or TIFF is what you want. Which one is more or less up to you. They are both non-destructive, and support all Photoshop functions and features. TIFF has wider universal support, but PSD offers some advantages in other Adobe applications like InDesign.

Both PSD and TIFF can be (moderately) compressed to bring size a bit down, but nowhere near the scale of jpeg compression - and it won't ruin your files.

Tiff are safe as long as you obviously save with layers.
Tiff supports alphas, saved paths and RGB/CMYK, 8, 16 and 32 bit images. I have never known an instance of any effect/filter that is not covered by a TIFF saved image, but I may be wrong (no doubt someone will correct me 🙂 ).

Things you could do to avoid big files eating up your space:
- Beware of smart objects with complex images embedded (particularly if you have a gigantic image, embedded in a smaller document. You get the gigabits and you're not making use of them).
- Consider using linked assets instead of embedded, particularly if they are shared assets (complex backgrounds that are found within multiple posters/banners, big images, logos, etc..), also make use of those CC libraries...
- If you're using smart objects but never touch them (eg: no filters, no transformations, no adjustment), consider rasterising them.
- Also, if possible use vector graphic elements over their rasterised counterparts.

I know most of it you probably already know, but just in case 🙂 ...