You should finish paving any paths, such as from the stairs to the lower patio. I would pave the area directly in front of the patio door out to the slab at the base of the stairs. Stepping stone paths should suffice for the side of the house. Remember that people will take the shortest route. You may need to use a shrub to block a shortcut.

I doubt anything will grow well beneath the stairs. It looks like that will have dry shade. Definitely fill in the missing soil so water that does get in doesn't pool against the house, and since you are digging make sure to add plenty of compost to every bed.

There are different types of shade from light shade that occurs beneath young trees during the middle of the day, or under tall, open canopy trees with dappled shade, medium shade is bright but allows little to no sunlight through, to deep shade found beneath structures or evergreen trees. Even woodland plants grow and bloom better when they get more light. So note how much sun actually gets to the area under the stairs. Best reliable plants for full shade are ferns, with the Lady Fern being somewhat drought tolerant. Japanese pachysandra also tolerates full shade as does Mondo Grass (Opiopogon ssp.) If the rest of the beds in front of the patio get part sun there are lots of plants to choose from.

Don't do the rocks!! Ask me how I know. With that small area you will not spend a fortune on mulch, mulch is cheap and you don't even have to mulch every year unless you like the "fresh" look. OR, do ground covers. Easy peasy. If you're going to do rocks around the covered deck, then do some snazzy big planters. That's what I have in front of mine. That and hosta. They grow thick, I don't even need mulch . . .

Thank you for all your suggestions! Always a work in process.

Due to I pinkmountain's comment I re-read your question. While rock/gravel does seem the easiest solution for under the stairs, it's only viable for under the lowest steps. And, I have no idea why mulch in your front yard is costing you a fortune each year. One should lay down mulch only the first year of a new planting. Most plants, even winter-dormant perennials should fill out and cover bare ground by the third year. Each year after the initial planting add an inch of compost (not mulch) between plants in the spring. IMO, it's much better to fill in between young plants with low growing annuals (less than 12 inches tall) such as petunia, French marigold, verbena, Madagascar periwinkle and dwarf zinnia.