Prior experience: None, never been that handy :-p
Problem #1: Water leaking even when unplugged. Determined this was a problem with the water inlet valve as it was leaking anytime the water was turned on, even when the machine was unplugged and not running. I followed along with a video on replacing Water Inlet Valve. Straightforward and easy and only took about 10 minutes after I figured out how to open up the top of the washer.
Problem #2: Wash bin thumping against side. Got some great advice looking around the interwebs and through forums that this is typically caused by a worn out snubber ring and/or weak springs so I decided to replace both. Fix was more involved and included removing the drive belt, the top and front panel, the motor, the 6 old suspension springs, taking the washbin out, flipping it over, loosening the 6 bolts on top until the snubber ring could be removed, replacing it with the new one, and putting everything back together with the 6 new suspension springs. Since I had never done anything like this it probably took around 2-3 hours, especially since I had no locking pliers or pry bar to help me get better leverage putting the suspension springs back on. If you find yourself in the same situation, I wish you luck and try to make sure any little kids are out of earshot so they don't hear you cursing as the spring slips just before it latches in for the 5th time.
Happy handymaning (or handywomaning) everyone!