Anytime I asked my friends in the UK what to bring to wear the answers were always the same: layers. Season didn't matter - it was always layers. I've found that fleeces are very useful.
Another friend told me not to put my "woolens" away until after May becasue it can be a swing month!
I am from northeast Ohio. I am used to cold. Last May in the UK it was about 70-72 degrees. I was outside working in the garden and the villagers who saw me said it was just too hot to garden. My thought was huh?

It's what you are used to.
If you are leaving the US on Monday, I wouldn't be too concerned about clothes. You'll figure it out once you are here for awhile. (Are you bringing the adorable tux?)
Congratulations on receiving your visa. I think many of us who watch this board were holding our breath for you. Please don't disappear from UK-Yankee after you arrive in Scotland.