Stuff to look for
Coolant blowing out of the reservoir cap is a main one, it lets you know when your egr cooler is going out/head gaskets going south.
Fuel pumps like to take a crap around 100k miles so get a fuel pressure gauge, anything below 45 psi will piss off the injectors untill they commit suicide.
Pull out the egr valve and check to see if the inside of the intake is wet, clean the valve also.
I think just about everyone runs rotella T6, i change it at 6k miles.
ONLY use Racor or motorcraft (same) filters, oil and fuel.
May as well change fuel filters right away, one in the pump and one in the fuel bowl.
Look up "blue spring mod" and do it, make sure to change the rubber gasket cuz they leak eventually.
Save up a $3-5k in case you need to delete the egr, get head studs,new gaskets, oil cooler. Unless you can do the work yourself.
I guess most important first off is get a scanner on it to find any stored trouble codes.
Thats all the basics i think, im tired so maybe missed something.
I wish you the best of luck, a lot of 6.0's do just fine for many many miles. Others nit so many. Lol
Oh
If you plan on running aftermarket tunes get an SCT TUNER. Also you may as well have the egr delete, head studs and new gaskets done before bothering with tuning. Some guys have gotten away with running somewhat hot tunes on stock motors but they are few and far between and just waiting to blow head gaskets.
Tons and tons of good info here and its easy to find.
Welcome!