What other brands/models should I consider up to this price? Røde NT1/NT1A? sE electronics X1? Shure Sm57? Audio Technica AT2035? Any AKG or Sennheiser?
You don't really want a Shure SM57.
There are two types of mics in your price range and for your experience level:
Dynamic mics can be OK for recording if you have nothing else. They are also used by pros in certain application when a particular sound is desired. They are also used when SPL is high - such as mic'ing a Guitar or Bass cabinet. Shure SM57s are commonly used in the studio on Snare Drums and Guitar Amps.
They're also used in live situations as well (SM57 and SM58 are the workhorse industry standard for most live mic'ing, and most other brands are simply variations on that established theme).
But on acoustic sources - especially quieter ones, for recording, a dynamic mic is typically not the go to choice unless a very specific sound is desired.
So you want a Condenser.
Condensers come in two basic types - Large Diaphragm or Small Diaphragm (though more recently we've seen more and more "medium diaphragm" mics on the market).
The primary difference is that SDC mics tend to have less off-axis coloration. This, and their smaller size, makes them ideal for use in stereo pairs where you want to capture information "from the sides". They're also great for live use when you don't want a big mic in the way of someone's face or hand, or when you have to mount them on stands above a drum kit - the heavier LDC mics can topple over the stands and damage the mic!
Another consideration though is that apples to apples, SDC have more self-noise (which is an important factor in Classical Guitar recording) however in your price range, none of the mics are going to be as quiet as the upper end models.
Ideally, which you choose would be based on your recording environment.
Looks like 200 Euros is about 213 USD at this moment.
Here's what I feel like you need:
1. Condenser mic.
2. The lowest note on guitar is 82 Hz roughly. While the body itself may produce some lower frequencies that means you need a mic capable of getting down there. So the frequency range you need is at least 80hz to 20,000 hz (20khz).
3. Classical Guitar is a quiet, and somewhat delicate instrument in a lot of ways, and if your recording environment is not 100% noise free, a mic that requires higher gain (SDC) is not as good a choice nor is one with higher self-noise. Likewise, it's imperative that it have a bass cut feature for getting rid of any air, air-handling, rumble, etc. noise. That needs to be at 80hz so it doesn't cut any guitar notes.
The Audio=Technicas are on sale so hard to tell what they usually go for, but the only thing I really see that meets your needs and price range is:
The ATM 450 would be a good choice as well, though at its current price of 219 it's topping out your limit, and since the 4040 is around 225, you might as well go for that if you can swing the 219.
So the ATM 2050 looks like the most likely candidate to cover your needs and to still be in a reasonable price range where you can get it (Amazon Europe? - it looks like it's $229 usd normally so if you can snatch one on sale...). It has a couple of additional advantages such as switchable polar patterns (which are great to learn and may provide more options for you getting a good sound).
I would dare say though, any mic in this price range that is that feature-laden also probably made some trade-offs in terms of sound quality.
But let's face it, if you're stuck in this price range, you can't expect miracles. Instead I would focus on LEARNING - learning about microphones and how to get the best sound with what you have to work with, learning polar patterns, placement techniques, and so on. So it's a great "learning mic" for not breaking the bank, assuming you can get it at that price where you are.
And the advantage of the 2050 with its bass cut and switchable patterns is that it could be used for other applications as well, which would make it a comparatively inexpensive all-purpose mic for you to learn on. If you upgrade in the future, you will have still gotten your money's worth out of it.
Honestly, any other mic in the price range is going to be a compromise. But I'll also add that I've never heard any of the SE mics personally, and the experience I have with AT and Rode are for mics above your price range. So the 2050 fits your needs "spec" wise - whether or not it gives you the sound you want is another matter.
I'd recommend buying from somewhere that has a return policy that will let you try the mic, see if you like it, and trade it for another if you don't.