Suitable Ivy

Sun? Shade?
Sun, for the trellis - look at trachelospermum jasminoides. "Star jasmine" is what it's called in the trade (unfortunately, but there's nothing wrong with the latin name, and it's not a jasmine).
Shade, for the trellis - ivies, several to choose from, and honeysuckle - evergreen ones such as lonicera henryi 'Copper Beauty', plus some evergreen clematis such as the c. cirrhosa cultivars, and clematis 'Early Sensation'.
For the wall, if it's in sun, then some campanulas, also many climbers, including ivy.
In the shade, then campanula portenschlagiana (although it's tough enough for sunny sites, too, once established), and the smaller leaved ivies, such as hedera 'Tres Coupe' (sorry can't put the French accents on), or H. helix 'Goldheart' (but keep it in check)

If its Ivy the roots will cling into the mortar and eventually destroy the wall.