First of all, I will say that removing plants from the property is illegal where I live. Some people choose to do it, anyway, I'm sure, and while many probably get away with it, I personally know one woman who was required to "restore" the property to the same condition it was in when the buyer first looked at it. That cost her a couple thousand dollars, as I recall. So, you might want to find out whether the law in your area says anything about removing in-ground plants from a property that's being vacated.
If you decide to move some or all of your plants, you would probably have to plant them in containers and then replant them at your new home. Alternatively, you could just keep them in containers for the duration of their lives. A plant suffers a certain amount of stress every time it is uprooted and replanted. Even moving a plant from a small container to a larger one causes it to suffer a certain amount of stress. The reaction to the stress is that the plant drops any flowers or fruit it may have produced, to enable all of its energy to be directed toward the production of new feeder roots. Only after the roots are established will the plant again begin to produce flowers and fruit. So, before digging up everything, you may want to consider whether the remainder of your growing season will allow sufficient time for the plant to recover from being moved.
"Isn't it enough to see that a garden is beautiful without having to believe that there are fairies at the bottom of it too?" - Douglas Adams