Howto setup LogShipping properly I want to use logshipping to transfer large databases (400-700 GB size) from Server (and storage) A to Server (and storage) B.

I tried this several times and it worked. But I have questions about some details:

While using LogShipping, the only Log-Backups that can be taken are the backups that the logshipping process creates. So other backup software or jobs have to be disabled in advance. 

In case I setup log shipping, the initial fullbackup that is required, independantly wether I take and restore it manually in advance of the logshipping setup or let the logshipping setup create and restore it for me, will take a while, at least one hour or more, to be finished, and additional time to be restored on the secondary. I have already tried both options with success for smaller dbs.

My question is: If I set up logshipping for a large db and need to stay able to do a point in time recovery, what will happen in the time between taking the initial full backup and the first log backup taken after the restore of the full backup has completed? Is there something like a gap in backup? Before the setup of log shipping is completed, I guess there is no backup configured at all, so will I lose thios period of time? Or will the transactionlog just keep growing until the full-backup-restore part has completed and the first log backup happens?
You can keep taking log backups on the primary server during full backup and restore to secondary. When you set up log shipping restore full with no recovery and all the log backups (taken during full backup restore) with no recovery. 
When you are caught up you initialize log shipping.