Lapua does not make any brass as of now for any of the 404 jeffery based rounds..If you want equal quality brass that is made..ADG brass is every bit the equal of lapau brass and they do make it for 7SAUM..
https://atlasdg.com/product/7mm-saum/As for COAL for your rifle..thats up to you, if you need to fit a magazine then you build your ammo slightly shorter that mag length so it will function properly, if you single feed or modify the rifle for longer mags, then you can use where the lads are in your barrel to set COAL... to give an ice, I have a rifle built for 300rum(404 Jeffries case big brother to your scum), SAAMI prints set coal at 3.6" max..I have the rifle throated for running the heavies, so I single feed and load out to 3.950" for my 230 berger LR load, for my shorter hunting load based off a barnes 200 grain LRX I have it setup for mag length in the accurate mags 3.850" CIP pics type mags and the 200's run at 3.760"... the advantage of running custom is you can maximize cartridge space while getting max performance from the bullet, the case, the powder and the cartridge combo...
ETA: A final though on reamer choice, you need to discuss with your gunsmith what is best for what you want to do..and you need to be honest with him about your loading abilities, if you have no plan to spend the time to build quality ammo matched to your chamber, there is no reason to use more then a SAAMI match chamber ream...If you are going to build the ammo and everything it entails, then first you need to decide on the actual use of the rifle, then what bullet/bullets best fulfill that use and finally get with the smith and decide a twist and a reamer that makes that possible...
As for which bushing you need, you can't know that until you get the brass you are going to use and measure it..generally you will want at least 3 bushings for subtle differences in brass thickness anyway, and you may want more, I currently have 6 bushings for my one LR rifle..