I have a 15 year old washer and 20+ year old drier (they both have fake wood veneer on them). I bought them used a while back, so I do not know their life cycle too much. I have fixed both on a couple occasions. Recently my washer went out, and I had to replace the whole water pump assembly. Repair took a few hours plus another in parts hunting and driving. It cost me like 50 bucks total, and that was a major repair.
Point is, the older units are easily fixed for cheap. If it is truly beyond repair, get something cheap and uncomplicated, I have maytags which I have liked. But the old ones are fixable, have parts readily available, and are likely better quality.
New efficient washers don’t wash clothes for crap. How much water do I save if I have to run my washer twice? From my experience, new driers take twice as long and dry half as well.