You might be facing a bit of an issue here. I'm assuming you're planning to do log shipping after a restore to get the 2000 database to 2014? The problem here is, you can't restore a 2000 backup onto a 2014 instance. You'll have to go through a 2005, 2008 or 2012 instance first. This is not something I've done personally, but I suspect it's going to be quite difficult. Instead of a zero-downtime switch-over you might want to plan for one with down time so that you can do the necessary hop. How big is your database?