Great question! You’ll want to plan your outdoor succulent garden based on your zone. Since temperatures in New Jersey can get quite cold, you’ll either want to plant succulents that are cold-hardy, or in containers that can be brought indoors.
As for when to plant, this also depends on the type of succulents you want to plant. For cold hardy succulents, you can plant after the ground has thawed enough to dig, and the temperatures are no longer freezing at night.
When I initially planted my own cold hardy garden in Utah (Zone 5) I started at the end of March and they did extremely well.
If you opt for tender succulents (those that will not tolerate long periods of frost), you can plant them any time indoors and move them outdoors once the low temperatures are consistently above 40 degrees.