Boxwood is nice but very slow growing. Nandina (heavenly bamboo) works well and has good winter interest with berries and orangey new foliage. Nandina domestica is too tall for your requirements. N. domestica 'Compacta' may be too tall as well (about 4-5'). N. domestica 'Gulf Stream' is about 3-3.5' and very tidy. Do you really mean giant arborvitae? That is a monster - probably grows 3' per year, not 3' total. There are other evergreen shrubs that you might consider, but first determine if you want solid green or the more multi-colored foliage of the Nandina. There are dwarf Pittosporums, Rhaphiolepis umbellata 'Minor', and probably some others as well.

I'd not hesitate to get the smaller plants. If they are planted in appropriate soil and given adequate irrigation until the rainy season (and you have to keep checking them if we have dry spells during the winter - you cannot let the root balls dry out and those root balls will be fairly small) they should do just fine and yes, will catch up within a relatively short time.