if you're getting flukes, make sure you get a model w/ min/max recordings... that's how you'll find your problem. I do this stuff for a living on 480AC down to digital controls and chase noise problems on drives all the time. An 87 is a good meter but I usually work w 189's & 289's. Overkill for the house.
Burned appliances are usually due to a voltage drop causing higher currents across fixed loads. That's a loose connection, though I was home once when a sensed a drop in the lights. I got my 189 on the circuit, and kept it there for a few hours. Watched it drop to 48VAC. A min/max reading will catch that. I was catching a loose connection in a transformer from edison down the street that actually started a fire in my neighbors house... literally. They had a cheap surge protector for their computer stuff that caught fire and burned their carpet. I talked w the edison guy that showed up & he copped to it when I explained who I was and what I did, and no, I didn't have a claim since I shut down the house as soon as it happened. Otherwise, that's when appliances burn up.
You'd want to measure each leg coming into the house, or pick a leg on a suspect breaker. You need to put the meter at the end of the branch on the last outlet since a loose connection can be anywhere along that branch. With only one meter, you'd work your way back on the daisy chain. It's either that, or start in the middle, and work your way forward or back, each time "cutting the deck in half". I've done this kind of stuff using 8 or 9 meters at a time on complex circuits. Industrial 480AC down to low voltage drive boards. If you burned something plugged into a particular outlet, it's easiest to cut off a cord, strip it, plug it in and throw you leads across the wires and then set the min/max on AC. You'll get a tone every time a new minimum or maximum voltage gets recorded. Do it that way, and you won't disturb the problem by moving wires around. It's pretty important not to disturb the problem by not moving anything until you narrow it down to a tight area. Once you ID it, then you can start opening stuff up. I've had meters on circuits for days trying to catch an intermittent problem. A word of warning; I work on this kind of stuff hot, and situational awareness needs to be very high.
my money would be on a loose connection or a pigtail connectors w 2 or three wires in it that's heated up and cooled enough times to cause thing to loosen up inside. Maybe a broken wire that arcs when it gets hot, then cools down and makes up. Seen that too. Hopefully there aren't any pigtail connections behind walls, in between outlets. I've seen that done... splices where there shouldn't be. A fluke w a min/max recorder will find it, and two or three meters make it go a lot faster. At any rate, a good meter is a good investment.
good luck.
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