[Nabukadnezar]

Let's take as an example NO₂°, and nitrite.

Which of these four ways would be best for me to continue using?

I believe the answer is "the third one".

Are there other ways of drawing resonance structures?

As a secondary question:
Why isn't Nitrogen Dioxide shown as a resonance structure on ChEBI, PubChem and ChemSpider?
https://www.ebi.ac.uk/chebi/searchId.do?chebiId=CHEBI:33101
https://pubchem.ncbi.nlm.nih.gov/compound/3032552
https://www.chemspider.com/Chemical-Structure.2297499.html?rid=7ab4e38e-199c-4934-aa6f-dc243295365c&page_num=0

[AWK]

These pages do not show the correct electronic structure, even if they try to.
But many relatively simple programs have trouble with the octet rule at the nitrogen atom (just at nitrogen atom).
Look for the correct electronic structures of nitrogen compounds on university VSEPR pages.

Structures in the first line are identical

[Babcock_Hall]

Your bottom structure appears to be the nitrite ion, NO₂^1-.  You can draw a resonance form of this as well.

[Nabukadnezar]

Your bottom structure appears to be the nitrite ion, NO₂^1-.  You can draw a resonance form of this as well.

Isn't that what I drew of it though?

[AWK]

Resonance structures do not contain curved arrows. Your nitrite ion drawing only shows the movement of electrons from one structure to the other one, not the resonance structures.