I've incorporated in Oregon.
I was the incorporator, and I simply held an organizational meeting and issued shares to myself. Is this legit? Do I have to register these startup stocks in some way? Or is that only necessary for (some)private and public offerings?

Any help would be appreciated!

Actually, most small Corporate clients especially closely held corporations generally are not required to register these initial start up shares formally.

If, however, you have formally requested investment from the general public, then I believe that you may fall under 1934-1936 Securities Act and may be required to register your shares.

I would strongly urge you to consult your tax professional to determine your State obligations in this circumstances.

However, based on your situation it appears that there is no formal requirement to register the shares.

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