Multimeter recommendation?

Buy a cheap Harbor Freight meter if that's all you're doing.

https://www.harborfreight.com/7-function-digital-multimeter-63759.html

Buy the best you can afford. Frequently, when you have an electrical problem, others here can suggest tests to be made to find the problem. You may not know how to do the tests but others can guide you through it. Meter readings are essential for a rapid solution. No meter, no solution.

Also, in the course of doing the above, you will learn tricks to put in your memory bag.

P.S. having an amp meter can be very helpful.

How much amperage does it measure? Most low to mid priced meters will only measure small amounts of amps so that function is largely useless. As noted above just buy something cheap as it will do more than most of us need.

Is the meter a clamp-on amp meter? I rarely use my amp meter, but it's very handy to have. The Harbor Freight meters will do a decent job for simple continuity and voltage testing, but nothing sophisticated. The level ability of the meter should match your level ability. :) For simple continuity and voltage testing, a HF cheapo will work as well as a $150 Fluke. But if you need more...

DC amperage is very hand around an RV where nearly everything is DC. Is this a clamp on amp meter or do you have to insert the probes into the cirucit? I prefer the clamp style as it's much easier to use and will read much higher currents. If you ever need to measure DC current from a solar array or to an inverter you will appreciate the clamp DC meter.
I wouldn't buy anything electrical from HF. If you're going to invest in a tool invest in a good one. Fluke is the top of the heap but I'd take Klein, Southwire, or Ideal any day.
Keep in mind, with cheap HF meters, you will have live electrical power flowing thur this device. A cheap meter that blows up in your hand is a really bad deal.

Thanks for all the comments!

I didn't mention this in my original post, but I am closing on a house next week so I figure even if I didn't have the refrigerator issues, a good multimeter will still be very useful.

Roger--according to the info on Home Depot's page, the 390 can measure up to 400 amps DC.
fj12ryder--it is a clamp-on meter. My electrical knowledge is a bit limited but I do know I want the ability to measure current in addition to volts and resistance.

We have Fluke and Amprobe clamp-on meters we use primarily for accurate current measurements. For quick, general troubleshooting we generally use one of 3 or 4 red Harbor Freight VM's we picked up for free a few years ago (currently sell for $6.99). DC volts read to .xx and they're reasonably accurate.

There are a number of inexpensive clamp-on ammeters with test leads for measuring DC and AC voltage, that also have capability to measure both DC *and* AC current (using the clamp-on, not the test leads), available on Amazon. IMO these units are the best, all-around, single device for general RV troubleshooting.

That "390 meter" from Home Depot would serve you well.

I’m an EE and have used lots of lab equipment for my job. At home I have a couple of DVMs and even an old analog one with a clamp-on current measurement capability. With that said, easily 80% of the measurements I’ve taken at home or RVing are simple voltage measurements (both AC and DC); the other 19.99% are resistance measurements (usually just looking for continuity); and the last 0.01% are current readings. My recommendation is to get a voltmeter and carry it, if it’s a cheap one it will probably do everything you ever desire; if you buy a nice expensive Fluke you’ll be able to admire it and be proud of it, but RV use probably won’t distinguish between the two.

For starter, a cheap $10-20 unit will be fine.

Checking amperage is far less commo but even the cheap ones will typically do 12v up to around 10amps. The downside is you have to put it in the circuit. The more expensive clamp on meters don't require the wires to be disconnected.