Answer: What a lovely project! Unfortunately even the lowest of maintenance plants require a modicum of care in order to look their best, especially if they are subject to constant scrutiny. The most important thing you can do to ensure success is to take care of the soil, adding organic matter wherever possible and using an organic mulch to help feed the soil as it breaks down over time as well as holding down weeds.
Having said that, the lowest maintenance and healthiest plants are those well-suited to their location. On your list, daylilies (Hemerocallis) and sedum are generally very resiliant, as can be some of the old shrub roses. Hybrid tea roses on the other hand, tend to be a bit more work. Shasta daisies may do well, however in my experience they require rich soil and division very frequently in order to perform their best.
Instead, you might consider Black-eyed Susans and purple coneflowers (Echinacea) for that daisy-type flower and mid summer color. You might also try snow crocus, crocus, daffodils, and a few tulips for early spring. Perennials to consider might be candytuft, dwarf iris, Siberian iris, nepeta, chives, foxglove, achillea, daylily, purple coneflower, Black-eyed Susan, veronica, salvia, coreopsis "Moonbeam", coral bells, sedums, smaller asters, and plumbago. For winter interest and structure, you might consider some dwarf shrubs such as the summer blooming spireas, or perhaps some dwarf conifers. Vines to consider would include the smaller types of clematis (this may be what you are thinking of on trellis); perennial sweet peas however tend to run rampant in all directions unless you are willing to tidy them frequently. Most other perennial vines would ultimately be too large for your space. Space will also be an issue, since even those tiny perennials can grow quickly!
To help you in your planning and in the ongoing maintenance, you might wish to look at a couple of basic books. I particularly like the Dummies series for straightforward, helpful information. "Gardening for Dummies" by Michael MacCaskey (ISBN 1-56884-644-4) will get you started, "Roses for Dummies" by Lance Walheim (ISBN 0-7645-5031-4) will answer all your rose care and pruning questions, and "Perennials for Dummies" by Marcia Tatroe (ISBN 0-7645-5030-6) will help with the smaller plants. Of course, you can always check in with the Q&A and its database, too!
Good luck with your project!
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