I like to try and avoid buying Capital ships with the UK if at all possible.
Sometimes it is unavoidable, and I kind of like the 1 dd, 1 trn, 1 ftr buy on UK1, but sometimes you may need the UK AC right away.
I usually send the UK fleet to Sz 8 and then merge with the US ships in round 1. I buy the AC with the US (possibly another ftr as well) and then on Round 2 merge the fleets in Sz 12 and take Alg.
Round three the Brits go to Norway (new trns placed in Sz 6) and the US AC/ftrs and possibly a DD following for added defense with the UK BB and DD. It really depends on the German threat. While the US BB and new naval buys from the US go to Sz 12. From here, the US can continue to supply Afr with troops while the UK focuses on Nor, then Kar.
By Round 4 or 5 you can shift the US north as well, since Afr should be well covered, but I actually perfer to keep supplying Afr (since you need less trns)or then shift the US to Med or to the Pacific. But before you shift make sure you’ve killed the Baltic Fleet and the Med fleet. I usually target the Baltic for round 2 or 3 and the Med for round 3 or 4.