In my opinion...
1. Thermoworks makes excellent thermometers and pH meters. Call them for openbox discounts etc. Pricy, but you can use for brewing, BBQ, and numerous other temp related projects.
2. Turkey frying thermometer (Walmart, etc). Cheap and adjustable.. long stemmed and have a clip to hang on pots, etc. Love them. May not be accurate enough for mashing tho.
3. Digital thermometers that have a cable probe are definitely subject to problems if the probe gets below water and liquid invades the probe area where the cable meets the curved SS probe. I've had good experience by submerging the unit beyond the probe in very hot cooking oil and letting it bake in a hot oven so the cooking oil gels. Then to be safer (?), I add a long piece of shrink tubing. Not sure how effective that is as the hot wort could loosen it. However, with these.. just don't let water/wort get into the probe.
I've had a couple of TAYLOR probe thermometers for years and never had one die. One for BBQ and one for brewing. I get mine at Target.
That's my arsenal and love them all