A landscape pro that could work for you might be a Landscape Architect, Designer or Contractor. The LA is a licensed professional, trained in grades, construction, materials, and much more. Their fees are usually fairly substantial, reflecting the educational and licensing requirements. They may or may not have a real knowledge of plant material or be particularly creative. Where I live, there are no requirements regarding calling oneself a Landscape Designer. They run the gamut from totally unqualified to very talented. Some Landscape Contractors can also have a terrific understanding of design and horticulture.
LAs really earn their money when there are formidable site challenges or ambitious construction projects. In your case, I think one of the latter two might be a more likely fit. Why are the shrubs and trees dead? There are plants that like shade and others that like sun, others that like both, and some that tolerate poor soil. Poor soil can be improved. Overgrown areas that need to be thinned or removed need someone with the knowledge of which, why and how.
That can vary pretty widely I suspect. Maybe 75-150 for an hour or so or 50-125 an hour in this economy, depending on area. With my clients, I give as much of the most pertinent information I can, for as long as they wish to engage me, include some rough sketches if appropriate, maybe demonstrate pruning techniques. If they like, I also will provide some sheets on pruning, maintenance etc. that I wrote. Actual commissions for design plans are priced differently, though.
Define your areas of use. Any lawn, patio, play, cooking areas? Figure those out then deal with the remaining areas with mulch, ground covers, perennials, shrubs, trees. You could read about planting design and come up with something satisfactory as far as general structure, but selecting the right plants to fill those niches and conditions is very challenging. A knowledgable and talented Designer or Contractor should be able to provide a good design for a reasonable price. That’s not to say, an LA wouldn’t. Maybe google landscape design and see what you can learn about them. See if anyone promotes low maintenance, natural or native landscaping. See some examples of their work. If you see one or more that seems to fit the bill, ask about a consultation and/or design.