Normally, my plan cashes out the first account, rolls over the cash, and then I choose what to buy in the new account. Where you are moving specific assets, I believe that is called an in-kind transfer. There are no particular tax problems with doing that. You will be taxed on the market value of the conversion as of the day it happens. Once the assets are in the new account, anything you do in the new account has no particular tax consequence, other than the normal rules that apply when withdrawing money (5 year clock, etc.)
There IS a potential issue with the wash rule if you sell securities for a loss outside the IRA, but then buy the same security inside the IRA, but that is not what you are talking about.
