@JohnA
The migrations depend on your specific circumstances. For instance, are you migrating from shared hosting or a vps, and if you have root access. Other things such as if you are migrating from cPanel, have the full cPanel transfer backups been disabled by your host etc.
Worst case we can work with you to perform a manual migration for a nominal fee, but most cPanel -> cPanel migrations are done free of charge.
As far as the website traffic, our VPS's are designed to handle surges in traffic up to a certain point. Obviously some things such as disk space, or ram consumption would cause operability issues (i.e. running out of memory). If you are simply experiencing large traffic loads that might spike your CPU we will make every effort to notify you first to give you a chance to make adjustments before we take further steps. If you are aware ahead of time of your busy season, or large advertisements then we would hope you would contact us to prepare ahead of time by adding additional resources etc.
Let us know if you have any further questions!