Which finish for storage box / tray?

I’ve just finished working on this storage tray thing. I plan to use it to store things I take with me every time I leave the house - keys, wallet, sunnies, that kind of thing. So it will see fairly heavy use. It is made of pink box.

what would be an appropriate finish to use that would stand up to this kind of (ab)use? I know that an oil based varnish is probably the hardiest option, but I’m not sure how I’ll go getting it into all the corners evenly without running etc.

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