When it comes to recording, your choice of microphone for the task at hand is a crucial decision. No two microphones are the same, nor will you be able to capture the sound of an instrument to it's fullest potential without some sort of knowledge of microphones and their placement. Important to note is that mid-range microphones are often more than enough, and going all-out for that Neumann is not a requirement to capturing excellent sounding tracks.
Generally speaking, there are 3 main types of microphones that will all possess different characteristics and applications: condenser, ribbon and dynamic.
Condenser microphones are generally more sensitive and responsive microphones. These mics usually have a lower SPL rating (these types of mics can distort if what you are recording is too loud or too close) and are usually best-suited for vocals, drum overheads, acoustic guitar, or capturing the room sound. There are many variations of condenser microphones (large & small diaphragm, pencil condensers etc.) but if you're just getting started, I would suggest starting with a large-diaphragm condenser in a cardioid pattern, as they have the widest range of applications in a home-studio setting.
Dynamic microphones are best-suited when in close proximity to the sound source. These microphones can usually handle higher levels of sound before distorting (higher SPL rating) and will be best-suited if you're trying to capture the sound of a loud guitar cabinet, a brass instrument, or a powerful lead vocalist. Dynamic mics usually are less sensitive, and won't generally capture as many subtleties and nuances as condenser or ribbon mics will.
Ribbon microphones are similar to a condenser microphone, but possess characteristics of both condenser mics and dynamic mics and will sit somewhere in between the two. Ribbon mics have been around since the early days of recording and do possess a specific warm sound. Ribbon mics were largely used to record vocals in the early 1900's and are still very common today. Ribbon microphones are excellent on guitar cabinets, used as drum overheads or for capturing vocals.
"That's great...but where do I start?"
It's important you first consider what you are recording. Are we recording a delicate vocal track or a cracking snare drum? Are we trying to capture the nuances of an acoustic guitar, or are we recording a screaming electric guitar through an amp? Condenser and ribbon microphones tend to be more sensitive than dynamic mics are, so unless you are using a condenser mic with an exceptionally high SPL rating, you will likely end up clipping the microphone and overloading your track. Using a dynamic mic to record a soft singer will not produce desirable results. This is why it's so important to choose the right tool for the job.
If you plan to record guitar cabinets, brass instruments, or acoustic drums, you will need at least one dynamic microphone. Start with a Shure SM57 or an Audix i5, both of which will do a great job of capturing the sound of the instrument at hand.
If you're in the market for your first condenser microphone, start with a large-diaphragm cardioid condenser microphone, such as an Audio-Technica AT2035 or AT4040, or a Shure PGA27 if you're on a tighter budget.
Just as it's important to develop an understanding of proper microphone techniques, it's equally important to use your ears while recording. Some of the best audio I've recorded is the result of creativity in microphone selection and placement, and trying different things to capture the best sound. There's no "one-size fits all" approach to recording, as every single instrument, voice, room will have unique characteristics. It's important to start with a basic knowledge of the different microphones and their applications, as well as a basic understanding of where to place them.
This is where a bit of experimentation and tweaking will come into play. When it comes to recording, there are no set rules or formulas to follow to get the "perfect" sound every time. There are several external factors that will also determine the quality of your recordings, such as room size and acoustics. Also, be sure to take a look at the article entitled Prepping the Room for Better Recordings for more info on other factors that will affect your recordings.