MNL is indeed fun...........
You will be first to exit the aircraft so you should get to the passport gates first - clearly marked with "FOREIGNER", the immigration process is straightforward.
I didn't have the courage to ignore my TA advice to not fill in a travel declaration for each journey but was NEVER asked to show it.
Here is the link in case you are as authority-respecting as me.
eTravel
Airport transfer:
GRAB is the Uber of Manila
You can walk up to the GRAB stand, directly outside the terminal and book a ride with cash (plenty of bank ATM in arrival hall) or you can download the app and hail a ride that way. Warning - the free airport wifi does not carry to the Grab lanes so you will lose connection while waiting and won't know when your ride arrives - it is all a bit chaotic as you'd expect. Of course, if you have mobile roaming then no worries.
Our hotel was a $14 GRAB ride from the airport. The airport limo was $100 and was super luxurious.