Mic placement will be as important as the mic itself. From experiments, it seems dangling the mic straight down about a foot (.3 meters) to 18 inches (.5 meters) directly above the tongue drum is a good place to start. I would think your SM57 would work well like this.
You might also consider internal miking. The Hapi DuoFlex stereo mic is in your price range.
If the plan is to eventually use pedals, you might consider a piezo pickup. These work incredibly well with a steel tongue drum. They're not prone to stage feedback and don't pick up room noise. My Beat Root came with one installed and it's really nice with some processing. Here are some possibilities.
If you have soldering skills, you can also make a great one for $10-25.
Any mic or pickup is likely to need processing to get the impedance/EQ/levels right going into a board or USB audio converter. I have a Baggs Session DI. It's pricey, but sounds great. Here's a clip of the Beat Root piezo run through the Session DI and the Everest Delay/Reverb.