As always with any landscape design question, photos of the area are necessary to provide any kind of meaningful help. And we also need to know geographical location as well, as that can impact on what is suggested both in terms of materials/techniques and any accompanying plant choices.

Do you want to put furniture on the patio? It will not work well with gravel.

Pics... need to see how sloped.

Leave both areas to the pros. ..............: ) A big home joe mistake won't save you anything, but might just cost you a ton of time, energy, and MONEY. For the do over.

IMO on a slope the best is a deck to make the space level and useable. Seating in a gravel pit is never nice except around a fire pit for safety.

Wood chips or similar organic chunky mulch would be best/healthiest for the tree roots. Certainly you wouldn’t want to do anything that would impair the health of the trees, if you like the spot.