How much have you got to spend? If your limit is $150, moving magnet is all you’ve got baby!
Moving magnet or moving coil? There’s a bit to this but simply, almost all the best cartridges are moving coil designs. That isn’t to say there aren’t some great moving magnet cartridges, especially some vintage models. Rather, the best solution – technically – is the moving coil design, because of its reduced moving mass and therefore greater linearity and micro-dynamic accuracy. Lower mass means lower inertia and therefore better transient response and high-frequency performance. All of that translates to better dynamics, detail, lower distortion and more of that elusive ‘air’. I’ve written about this here.
Marketing departments have tried to convince people that lower-cost moving magnets are “as good” or “nearly as good” whatever that means, but they still have these inherent design limitations and speaking from experience, they simply aren’t as good. Because coils are technically better, manufacturers also tend to spend more on these designs, using better diamonds, more expensive boron or even diamond cantilevers and better coil wire. This means you can spend a ton on a good MC cartridge, but remember that a really good moving magnet cartridge will be better than a cheap moving coil. You get what you pay for.
The caveat here is that because moving coil designs generally have much lower outputs, you need very high-quality electronics and a step-up transformer to get the most from them. Don’t expect a really good moving coil cartridge to sound its best using a built-in or cheap external phono preamp.