NO! There are many different kinds of microphones, and each has a different use and purpose. Not every microphone will work in the same way and they don't sound the same. They are usually in a school's auditorium or gym or any stage setting. Check for what your school have before going out and buying one that you may already have access to.
Microphones can be a bit tricky, especially when you are working with a budget. You will run across a few different types, and each of them has a different purpose and strengths.
It is best to know what kind of recordings you are wanting to make before purchasing anything.
Look at buying guides for what microphone might work for you, then visit the set up that you are looking for and see how you might use it.
You may want to talk in-person with someone that knows about microphones, like going into an audio shop and explaining your situation.
Typically used for a stage setting, and they don’t require an external power source. They can handle a lot of loud sounds and are durable in different conditions, but they don't pick up sources that are more than about a foot away (only good for close miking).
They would be best suited for live recordings, especially if you plan on doing anything outside. They are probably the most common microphone and it is likely that your school will have access to at least one. You will need access to an interface to use one.
They require some sort of power source, like batteries or an external source via cable (phantom power). They do cost a bit more than dynamic and are more affected by outside conditions, but they do have a good quality sound.
They would be best suited for studio recordings, and indoor events; recommended if you are doing any sort of stereo recording, and find a matched pair of pencil microphones. Another option is a large diaphragm microphone that has different settings available. You will need access to an interface to use one.
Are a kind of dynamic microphone, they are similar to condenser microphones, but quieter because they do not pick up as much background noise. They have a softer sound, are not as able to pick up treble frequencies, and will pick up sound from all around (and figure-8 pattern), not just from the front.
They are more fragile than regular dynamic microphones. You will need access to an interface to use one.
Can do almost everything that other microphones do, except they do it when plugged into a computer. If you don’t have an interface or a mixer, and are going to rely on your computer for managing your audio, they are a good choice.
If you know how to manage your chosen DAW, you will have abilities comparable to if you had a mixer or interface, though it will be a little more limited.
Check the kind of microphone that is used, and what the polar pattern options are.
This site is only for suggestions and examples on recording equipment and software and suggestions on how to set up your recording equipment, not exactly what you should buy and not exactly how to set things up. Depending on your space, equipment, and live/studio setting, you will have to experiment for the set-up that will produce your desired results. Don't be afraid to experiment and go outside of the suggestions laid out in this site.