The most common repairs for washers and dryers are pretty simple to do if you're handy. However, since installation seems to be a slight concern, it's possible that you might not be handy enough.
Me: if I purchased an electric dryer, the first thing I'd do is take the case off of it (Very simple to do) and remove the drum, then clean the inside - before I brought it into my house. You don't want to find out you're importing critters (the same goes with just about any furniture, etc., that you purchase on Craigslist - I don't make such purchases. However, in some areas of the country, people are unloading half the stuff from their houses in an effort to erradicate things like bed bugs. A friend of mine who owned a rent to own type of place said they kept a lot of their returned stuff out in a truck because cockroaches weren't unusual.) I'd then thoroughly clean out the entire vent system on it. Altogether, it'd probably take an hour to 2 hours to make it "like new" mechanically. About the only things that go on them, besides the electronics on some models, are the drum rollers. $20 to replace them & you're good for another 10 years. Oh, and the heating elements possibly on an electric dryer.
Washer: even simpler to open it up and look inside the case. Usually there's only 2 screws, and/or a couple of spring type mechanisms that hold them together. The controls on the top unscrew (else for some brands, have little springlike fasteners that you pop open by inserting a putty knife under the control panel) - the control panel usually then tilts backward, and a couple of clips hold the entire case on - unclip them, pull the case forward, and it comes right off. A couple of simple wire disconnects for the door closed sensor (I'm talking about top loaders by the way.)
Check the inside, clean if if there's lint in there, and pop it back together. 20 minutes. Most common repair I've seen on washers is a a coupling that connects the motor to everything else - it's designed to fail (preventing other parts from failing) - relatively cheap, and simple 20 minute replacement. The difference between a washer lasting 30 years, and a washer lasting 7 or 8 years is often a $20 part every half dozen years.
MOST important thing if you purchase a used washer: BUY NEW HOSES FOR THE CONNECTION!!!