permesso di attesa occupazione

Dear Expats,
I have questions about permesso for work search after graduation. My study residence permit is valid up till end of march,2019 so should I apply for "permesso di attesa occupazione" now or wait till the expiry of my student permit?
My main concern is that can I get work contract from a company on ricevuta as these days it takes more time( normally 4 months after application) to get an appoint in the police office for finger prints?

I will really appreciate any information regarding these.
Grazie mille

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