@mmicha said in Where to start...:
Build out a site to site to a their datacenter and slowly build / upgrade things.
A lift and shift can be a good idea. But it isn't very likely. Taking applications that aren't well maintained on premises and just shifting them off premises is just "moving" a problem, it isn't addressing it in any way.
That doesn't mean that you might not benefit from keeping these applications in this way. It's not to say that colocation is bad. But you can't start with the assumption that the "less common" solution will automatically be the right one with no evaluation at all.