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The rules say "use 4 colours only".

I recommend that you find a nice tint and go with a light-to-dark palette.

I've started but I might give up the screen size is pissing me off

It really boils down to "git gud". With that said I'm not sure what your problem is.

Mind posting a screenshot?

I've given up now but basically all my plans would be ruined by too large graphics or text ect.

Then use smaller graphics. 16x16 sprites should be fine. It gives you plenty of detail to work with.