GIMP Version: 2.8.18
Operating System: Windows
OS Version: 10 Home 32 bit
GIMP Experience: New User

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Have said I will (try) to do a logo for a podcast. Image has to be 1,400 px square while keeping below 500 kb mark.
Is there something I should not do, or is there something I can do after to minimize the data size?

GIMP, Save for Web plug-in works fairly well.
Check this Six Revisions article and the links at the end for a few techniques you can use with GIMP.
Advanced Image Optimization Tricks
Also, consider using a web-optimized palette.
Image → Mode → Indexed, Convert Image to Indexed Colors

Obviously always save your logo in Gimp .xcf format, but then

Do some experiments, exporting with various settings.
For a multicolour, 1400x1400 px image, you might get this using various options.

TIF no compression - 5744k
PNG default settings - 1288k
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JPEG default 90 Gimp settings - 308k
JPEG 85 quality setting - 260k
JPEG 80 quality, sub-sampling 4:2:2 - 192k

For less than 500k file size, any export as a jpg will do.
Use the Gimp default setting.

Thanks.

Tried more and it seems the more simple the image the lower the data size. I sent the first one I did (which was very simple) to the guy who wanted it and he is happy.

I did a larger one first but it had to look ok at this size as well.

I probably put you on the wrong track. With your logo thumbnail there are only 2 colours.

PNG will compress lots of the same colour very efficiently. If the image has an alpha channel remove it, then a comparison of file size for a 1400 x 1400 px image

That's ok rich. I left it as is, saved as a .png. The rss picture has alpha in it because I had to 'colour to alpha' the white out and the 1400 square pic was only 108 kb
Like I said it was very simple. I didn't do any extras on the text or the pic.
Finally worked out the default etc when saving as a jpg but too late he has it online already.