So I'm going to build a rifle. I've had an LRB M25 receiver in my safe for about 15 years now.  And I've got a TRW barrel that has minimal throat and muzzle erosion, still registered "new" by USGI standards last time I checked.

So would a modern nitride barrel "likely" be better than the TRW USGI?  

And is anyone making new op rods that are top-notch?

I had LRB install a TRW barrel on my LRB receiver about 10 years ago because I didn't want to risk the warranty. They did a good job, still have the rifle and still shoot it on occasion.

I would go with a USGI barrel over an aftermarket nitride but that's just me. Some say nitride is every bit as durable as chrome lined; I don't know about that but I do know they work good on ARs.

Good luck with whatever you decide to do and don't forget to post pics.

OP, is this rifle intended for competition or just general plinking? I built mine for competition at Camp Perry and did pretty well with it. I used a medium weight Douglas barrel but if I had a TRW barrel already and in good shape, I would have used that. The Douglas barrel is not chrome lined but that didn't matter to me. For an Op rod, I would look for NM (National Match) or GI. Try Fulton armory for parts.

I don't have plans for competition, but I'd like a rifle capable of competing.

TRW got a waiver from cut rifling barrels to make hammer forged barrels for the M14.

The TRW M14 barrels are hammer forged and slightly thicker / heavier in the middle of the barrel, but only by a very small amount.

The thickness difference is very small, but the TRW barrels are very slightly heavier than the service barrels.

Awesome. Use it.

No.

https://criterionbarrels.com/products/m14/m14-m1a-usgi-contour-barrel/
This one could be just as good, or possibly better, but it's not "likely" to be better.
If you order a Criterion barrel, get one with chrome lining. There's no disadvantage (unlike with older manufacturing techniques in the 1960s which statistically resulted in decreased precision).

Idk. Haven't looked for any in many years.
If you have an un-cut (not welded-back-together after DEMIL) USGI op rod, I'd utilize that as well.

+1 on the Criterion for modern chrome lining.  

The old barrels sometimes have their chrome lining flake off in the throat at which point it’s not going to help accuracy.  

From what I read the modern chroming is a much better lasting product.

I have on Stainless SA Inc NM barrel. 22”
One Winchester 6118 marked chrome lined USGI barrel 22”
and one 18” Chrome lined Criterion barrel.  

They shoot as good as each other.   The SA Inc. gun is scoped and bedded in a McM M3A stock.  It is a bit tighter than the others but still has a 1in 10 flier up and right from the group.  I did a lot of testing and never eliminated that egg shape group but it was respectable.