The IR temp gun will serve you better in the long run as you can use it on a whole lot more than your coolant temp.
A decent one will set you back around $100-$200. Don't know if I would trust any no-name ones for less. You could save some bucks by getting a used one, I suggest Fluke, just choose carefully and get one with a useful range to you, and read the descriptions and seller feedback carefully so you're not buying a dud. The Fluke 62 mini I've owned for 20+ years still serving me well. Their replacement for it, the 62 MAX, lists for $110 direct from Fluke with free shipping. The 62 MAX has a range of -22F to 932F so it's good for a lot of automotive stuff except maybe extreme catalytic converter failure diagnosis, since those can run up to 1700F in normal operation. They could easily get much hotter if the mixture is off..
Richard