I understand twist rates, barrel length, gas system, and profile, but what about finishes ?  Do I want a barrel that is chrome lined, melonite, or nitrite finished ?
I am looking for a 16 or 18 inch mid length barrel for a new build but stuck on this last deciding factor.

First question, what is your plans for this build?  I normally like chrome lined, but have a couple of melonite barrels and they are just fine as well.  I would be happy with either, building guns is fun, but don't fall into the trap over the tech terms, define what you want to do and figure out what you need to do it, then go shoot the hell out of it!

Melonite is a brand name for nitride.

What degree of accuracy are you seeking?  If you want a match grade barrel, that will usually be "none of the above" but rather 416 stainless, sometimes 410 stainless.  These barrels will not last as long as chrome lined or nitride, but are easier to uniformly machine for very price bore and rifling.

Chrome lined may have a edge for high rate of fire protection of the throat and first inch or so of rifling.  It is blow torch effect of mag dumps, bunp firing or full auto that rapidly causes throat erosion and drop off in accuracy.  But chrome lining is a plating that may not be uniform.  Thus, it may degrade accuracy.

Nitride is not quite as protective from heat, but is very close to hard chrome in hardness and wear protection.  It also protects the entire barrel both inside and out from corrosion and is about ten times more protective than hard chrome in salt water corrosion protection.  Nitride does not alter the dimensions of the rifle bore and rifling, as it is a hardening of the surface of the steel, itself, at the molecular level.  It does not degrade inherent accuracy, as chrome plating might.

Others will differ, but I rank them this way:

For a true precision match barrel shot slow fire:  416 stainless.

For high rate of fire and absolute round count:  chrome lined

For everything else in between: nitride.

Flip a coin. 99 percent of shooters will not notice a difference over the course of the rifle's life.

This is good advice OP, only thing I'd add is that many of the Melonite/nitride/qpq manufacturers have a sub-moa guarantee.

Faxon does, their barrels are very affordable and they are active here, they're (RogueNathan) quick to respond to any questions and very helpful.

MicroMOA has the guarantee as well, are active here and helpful as well, a little higher price wise but build some of the best nitride barrels out there.

Ballistic Advantage is another top-tier melonite barrel manufacturer, they offer the sub-moa guarantee as well.

VooDoo builds nitride barrels also, they're cheaper than the above 3, and I'm not sure if they're in the class as I've never owned one, but others seem to have good luck with them.

There's a "barrel" sub-forum if you need more specific answers.

If you're not doing mag dumps, nitride is hard to beat, combines the accuracy of stainless and corrosion resistance of chrome.

Thank you gentlemen, as always great responses !