Most Durable Climbing Ropes

I'm looking for a rope that is very Durable. My Dad is very para about accidents where ropes wear and snap. He likes to scare himself by reading posts about ropes snagging on rocks. I have looked at Unicore but I'm not entirely too sure about it. I do live in New Zealand, this may limit my options.
Hoping for something that won't break the bank

The sheath percentage is a standard metric - that along with diameter should give you a good idea of the durability.

You will probably get more appropriate answers (with regard to what is available in NZ) by asking on some Australian forums like the crag or chockstone if those are still functional. Might also ask on the NZAC Facebook page.
as others have said, sheath percentage is a good measure, Beal’s Unicore technology is worth looking into and I believe the UIAA is developing a standard for edge durability. It might be just Edelrid, though. 

Seeing as this is mostly a mental thing - show him the video below and order one of these:

https://shop.epictv.com/en/single-ropes/beal/diablo-102mm-unicore?sku=BEAS18_ROPDIAU_GRE60 
 

In reality, double unicore ropes would be even better for cutting resistance. If you're fine with doubles: https://shop.epictv.com/en/products/half-ropes?f%5B0%5D=field_brand%3A1047 

Matt N wrote: Seeing as this is mostly a mental thing - show him the video below and order one of these:

https://shop.epictv.com/en/single-ropes/beal/diablo-102mm-unicore?sku=BEAS18_ROPDIAU_GRE60 
 

In reality, double unicore ropes would be even better for cutting resistance. If you're fine with doubles: https://shop.epictv.com/en/products/half-ropes?f%5B0%5D=field_brand%3A1047 

I just like to point out that this video shows a sheath slipping on a core after the sheath is cut.  If you’re attached to a line with an ascender, this is super relevant.  If you’re attached via a knot, it’s a little less so.  I don’t think that Beal claims that the Unicore adds to the cut resistance of the rope in any way, just that the sheath won’t slip if it’s cut. Is there a video out there of what happens with the rope in a more standard belay system?

But I do agree that showing this video to your dad would likely calm his fears, for better or worse.
For OP- agreed with above, look at ropes with higher sheath percentages (38% or more). Most rope manufacturers have a rope geared towards durability in the 9.8-10mm world.  Edelrid Boa, Sterling Pro, Mammut Eternity to name a few.

james Paterson wrote: I'm looking for a rope that is very Durable. My Dad is very para about accidents where ropes wear and snap. He likes to scare himself by reading posts about ropes snagging on rocks. I have looked at Unicore but I'm not entirely too sure about it. I do live in New Zealand, this may limit my options.
Hoping for something that won't break the bank

Well you could tell him:  "OK Boomer!"

We're almost in year 2020.  All climbing ropes are incredibly durable.  I'd go with whatever works best for your goals in terms of price, length, girth, weight and dry treatment.

And yes that quote is a great example of Kiwi common sense, even in representational government.