I bought my K80 second hand - it was originally fix-choked and multichoked later (before I bought it), later I ordered Teague bespoke thinwall extended chokes in 2x3/8 +1x 5/8 constriction.
Those are best made (once you hold them you get to appreciate the marksmanship) - thin like paper, dont add anything to the weight of the barrel...
...anyway - at first I have put 3/8 (0.015) in the bottom and 5/8 (0.025) above. But last year in August I attended a Fitasc Sporting competition at Steyr Arms with some incredible far targets (70m+). Tempo of competition was rather fast and toward the end I got somehow tired and since I wasn't there to win anything I didn't bother to switch from 3/8 in both barrels - worked like a charm, never looked back since. Now I only put 5/8 when shooting trap for 2nd barrel, otherwise 3/8 are there to be. I do shoot top 5% antimony ammo all the time tho...
If I would be starting all over again (I don't shoot much trap lately) I would choose fixed choke - in the range 0.012-0.018 (tight 1/4 - loose 1/2) with high quality shot, maybe 0.020 (1/2) that would cover softer shot as well.