Congrats on the new purchase. Hope she treats you well.
Starting an I/O is a bit different than an OB because you have fual vapors you must consider.
So as a general guidline, here is what I do.
Once I jump on the boat I turn on the Blower and let it run for 4 minutes or so.
I then finish loading everything and get it all situated during that 4 minutes.
I then make sure Outdrive is down enough for water depth (not all the way up).
Then take throttle and disengage the shifting by pressing the button and push it all the way to WOT, then pull back all the way and then push back to about 1/4 down.
Now crank engine until it starts and keep hand on throttle so you are ready to back it off a bit if RPM too high.
I then leave running with a bit of throttle (around 1500 RPM) until she is up to about 150 degrees (else she will stall on me).
Once done with all that, it is push off time.
Now some people will also pop the engine hatch and do the smell test before starting as well. I generally do that before dropping her in the water but it is never a bad idea to do that each time as well.
Basically, you don't want any gas smell before cranking or a spark could blow the hatch. These things burn fast once they start so don't let it get started
You should probably do a quick engine oil check and outdrive oil check regularly as well. Not sure if you need to do it each time you start it but once each day or even once each weekend is probably good.