New stuff.
I work in a store that sells appliance parts. I am not a service technician, but I sell parts to them all day long.
First the dryer:
Speed Queen makes the second best dryers on the market. In my opinion, Whirlpool makes the best. They are sold under the Whirlpool, Kenmore, Maytag, Admiral, Inglis, Roper, and a few other name brands. The good ones are easy to spot because they have the lint screen access on top in the back right corner. This is called a "Whirlpool 29 Inch Dryer" in the appliance field. They have been in production since the mid 1960s and are still made today. They are the best performing, most efficient, longest lasting, and easily serviced dryers money can buy. There are only 2 or 3 features I would really look for. #1, a drum light, #2, an electronic moisture sensor, and #3, a drop-down door. The drum light is a rectangular plastic thing on the back wall of the drum. The moisture sensor is a black plastic thing with 2 silver metal strips at about 4:00 on the back wall of the drum. This is the only appliance I can confidently say can withstand 40+ years of regular hard service and still be reliable. If you have this type of dryer, keep it. Look up a Whirlpool 29" dryer on Youtube and get videos to show you everything. They are simple machines that are easily repaired.
Second, the washer. SPEED QUEEN! There is simply no substitute for the quality and performance of a Speed Queen washer. The Whirlpool Direct Drive washer, like yours, is good competition to Speed Queen, but if you want new, go with the Speed Queen. I prefer top loading, but buy whichever you want because Speed Queen makes the best of both types.
There are other brands that are very good, like Asko and Miele, but having them serviced is a bit more difficult and they are very very expensive. Samsung and LG make the worst appliances money can buy and many service technicians won't touch them.
Good luck,
Dave