Congratulations on the great first ride! That's a big one with a new horse and it's great to have gotten through it so nicely. It sets you up for a lot of success in the future!
I can whole heartedly attest to the value of hand-walking a "new-to-you" horse on the trail. Is great to do it even if you've already ridden the trail. It is a huge bonding time for both horse and rider and you'll notice it when you're in the saddle.
Enjoy all the wonderful rides you have ahead.