I went through this process earlier this year.
I found an excellent repairman. He told me that he could fix my current washing machine cheaply ($40) but it would not last another year before it needed replacement. (18 yo machine).
Here's his speech:
Washers:
Front-loading washing machines are worthless - get a top loader.
All new machines are crap (except for one - see below). Most new machines have computers in them, and the repairmen don't fix those, and the computers are cheap anyway (google "rebooting the washing machine").
You'll be lucky to get 6 years out of a new machine (except as shown below).
If you're going to buy a new machine, buy one this year. New energy guidelines go into effect next year and it will reduce the cleaning capacity of new machines.
That being said, buy a Speed Queen, one of the AWN models.
http://www.speedquee...s/products.aspx
Speed Queen are used in almost every public laundromat. They clean the best, they're made of all steel (no plastic), and they will last a lifetime.
Ask any repairman about Speed Queen, and they will all say it's the best by far. Nothing else is even close.
Dryers:
The only thing that matters, is that the bigger the tumbler is, the more efficiently it will dry the clothes. Brand name doesn't matter too much.