I may have missed it, but is OP removing the fence for proposed planting?
Another vote for less is more, as well as integrating architectural (trellis, arbor, ect.) for help in screening and interest. Grouping of plant material logistically on property for screening but adds an open feeling for the owner, as compared to a long length of hedge.
Leyland Cypress offers many of the aspects the OP is looking for, specifically along that back fence. There's newer hybrid varieties that have several color variations (silvers, lime greens for example) and offer better pest resistance and growth habits in contrast to the original species, but also is fast growing. Arizona Cypress is another option to inter-plant.
Utilizing the neighbors existing landscapes will help with the budget, which I interpret the homeowner recognizes in the post. Keep in mind that fast growing means less stability.
Yaupon holly varieties are also good options, but much slower growth.
ISA Arborist FL
FL Certified Landscape Designer/Contractor
FL Green Industries BMPs
Last edited by Hortus; 09-05-2012 at 08:25 AM.
Reason: Forgot to add to original post