Tee into supply lines.

Two questions:

1) I need to tee into my copper supply lines in the basement and then send it up to my new attic bath. I have a good spot picked out to tee in. How do I measure and cut for the tee? Do I just mark the new tee and then subtract 1/2" for the tee to fit over the existing cut pipe? How do you pros do it?

2) I plan to run 3/4" copper upstairs, then have it branch off to 1/2" lines for the two lavs and the toilet. I may keep it 3/4" for the shower if the shower valve is 3/4. I have a unique situation in that I will have a separate filler for the tub (iron cast, freestanding) and then a separate valve for the shower (one of those kohler ceiling tile shower heads).

is this a good plan? 3/4" up with 1/2" lines to each fixture, then 3/4 inch to the shower and tub lines?

Thanks.

I know you want a pro's advice but...

I'd do it like you propose.
One bit of advice from an infrequent solderer: If you don't have enough play to get the tee on, then loosen some straps on the lines. If you still don't have enough play, then you can cut a large (~6") section out of the pipe and make an insert with a tee, pipe, and hubless coupler. The hubless coupler will eliminate the need for any play.