Most of the energy and money savings in laundry come from improvements in washer technology. So pick the washer first. Remember that except for style, there's little reason to replace a working dryer with one with moisture sensors. Look online for rebates from manufacturers and utilities and then consider:
Top-loading washers with a center-post agitator usually cost the least and wash the fastest. But wash performance is often mediocre or worse, and they use more water and energy. High-efficiency top-loaders don't have a conventional agitator, so they hold more laundry. They use less water and spin faster than conventional top-loaders, resulting in less dryer time and energy savings. Front-loaders are generally the most efficient, using the least water and spinning even faster. They also have large capacities. But 8 percent of failures or repairs reported by our readers were due to mold.
Pass on thermostat models; ones with a moisture sensor have done a better job of turning off the machine before laundry is overdried, so fabrics aren't subjected to unnecessary heat, and energy isn't wasted. Most full-size dryers can hold an average load, but choose a model with an excellent capacity score if you frequently dry big, bulky items. And stainless-steel tubs look impressive but don't improve performance.