Would I go chrome lined? Nitride? What would you suggest and why?

Nitride, for both longevity and accuracy.  A l9t has been in question about nitriding, but tests are starting to show it is a very durable treatment, and it is cheaper to boot.

That being said, can't go wrong with chrome lined. I have had exceptionally good luck with both types, then again I stick to known quality brands: chrome lined I run FN or LMT barrels, nitrided I use Lothar Walther or Ballistic Advantage. Faxon has an exceptional reputation for nitriding as well, just haven't gotten around to using them yet.

Cheaper is better if you plan on burning up a barrel.  

Mine is on an Armalite M15 Middy barrel.  Since the range is on summer hours and I can't make it there most of the time, I have no chance at burning up my barrel.

Well, Larue will replace it if you burn it out 

Quality of the steel is more important than nitride vs chrome. Get the higher grade CMV type steel, with either bore treatment.

In a HEAVY profile. Need thermal mass to soak up that heat.

Longer gas system to minimize gas port erosion.

Get a handguard with a big aluminum barrel nut, and lots of aluminum on the handguard to dissipate even more heat.

And a barrel of water to dunk the thing in to cool it off.

I have multiple Larue bbls and I wasn't aware of that. Sounds like my search my have come to an abrupt end.

PSA FN CHF chrome-lined.