engine flush?

You will need to change the oil & filter before starting the engine. There is no need to "flush" the engine. Be prepared to change the oil & filter again after 5-10 hours of operation to get rid of the loose carbon, bits of gasket material and dirt that got knocked loose when the head was changed.

DEFINATELY change the oil before restarting. To save a little money, you could leave the old oil filter on and just drain and refill what's in the pan if the filter isn't too old. Like Jrichker said, you might want to change it again soon with the filter because dirt might have gotten lose in the mean time.

Engine Flushes: Mixed reviews on those. They do clean out an engine, no doubt but they are usually mineral spirit based so they destroy the lube capabilities so I would never drive or put any real load on the engine with these in there. Some say they can dislodge dirt and the dislodged dirt can cause damage. However, it will clean up gunk like no other. If you are going to use one of these, run it with some cheapo oil and a new oil filter, then drain it all out and run some more cheap oil and a new filter for a while, then change it again because you can't get all the oil out in once change and the next oil change is going to act like a "rince" so it will need to be changed again.

Marvel Mystery Oil: I work at a shop and we keep some on hand because it is the only thing we have seen that will quiet down a noisy engine. Engine's with lifter rattle are often fixed with this stuff. Some run it all the time, with every oil change with no issues, but honestly, I would run it for a while, then do an oil change.

Mobil 1 has a "drive clean" conventional that has extra detergent in it. Good stuff.

Drain the oil out and make sure there is no coolant or debris in it. You can use one of those funnels with a screen in it when refilling it. Water/coolant will sink to the bottom. M1 is expensive. If it's conventional then just put new in.