I always do scout-monument-granary/shrine when I go Tradition. Usually another scout also before or after granary.
I might deviate from this if I completely ignore cultural/tourism goals, but here's my reasoning: By the time I hit Drama & Poetry and should get the Amphitheater up, there are so many other things I need to build, and at the very beginning I can only either build a worker or another scout. Sometimes I even try to build monuments in my #2 and #3 cities and take Aristocracy + Oligarchy first just so I can delay legalism for 3 free Amphitheaters. This has also worked surprisingly well for me. If you do Piety, you could use legalism for Opera Houses and instantly start building the Hermitage thereafter. I feel the lost hammers in the beginning are more than made up for later on. An early cultural ruin -> I still build the monument in cap first, and just take Aristocracy as the 1st policy. I still get the free Amphi, but benefitting from the cultural ruin, I'll also get to Landed Elite almost as quickly as I would normally by starting legalism. This does (very slightly) delay finishing Tradition, but I want to have Engineering researched by the time I do, so I won't waste even one pop of the added +15% growth, by having Aqueducts up at the very same turn. If a city is one turn away from next pop and I finish Tradition and don't yet have Engineering, that growth step would not benefit from the Aqueduct..
One thing to also consider about cultural play is that you don't actually need many amphitheaters at turn 100. So there's no obligation to madly rush to D&P because those theaters only start to really work once they're all filled with great works. So, consequently, I have seen that if I delay D&P until I am able to really fill the Writers Guild with specialist right away at completing it, my long-term culture & tourism tends to be better than it would with beelining the drama techs/buildings. Playing like this I do get the first 3-4 monuments up some 9 turns later than I normally would, but Tradition's natural increased tile expansion rate easily makes up for that. And in my experience, I am ahead on my tourism generation by late medieval when I play like this.
Usually when the traditional cultural approach around T100 would be to be build an amphitheater in all 3 cities, I'm building the National Epic and a Garden in cap, while 2nd and 3rd cities can build colosseums, markets or whatever, since I got the Amphis for free. Now The Writer's Guild is up, immediately filled with two specialists, and boosted with 50% right from the start. It works.