Rule number one of polar pattern selection: Choose cardioid!
Well, that was easy, wasn't it? Of the four main polar patterns you can choose from - omnidirectional, cardioid, hypercardioid and figure-of-eight, cardioid is generally the best pattern for most jobs.
There are good reasons for this. An omnidirectional microphone picks up sound from all around the room. This means that it will pick up other instruments, and even if there are no other instruments it will pick up a lot of reverberation.
The consequence of these unwanted sounds creeping in is that you will have to place the microphone closer to the sound source. And unless you want the unnatural sound of excessively close miking, this is not going to produce best results.
At the other end of the scale is the figure-of-eight microphone. If you point this at the sound source, then you must also consider that it picks up sound just as readily from the rear. So it's a mic that you can't help but point at and away from the sound source simultaneously. If there is sound coming from the rear that you don't want, it will be picked up in all its glory.
So cardioid is a good in-between choice. It is reasonably directional and rejects sound from angles other than its main axis. No-one ever got fired for choosing cardioid. (Hypercardioid combines features of the cardioid and figure-of-eight to produce a pattern that is more tightly focused than the cardioid, but at the expense of some unwanted rear sensitivity.)
But there is another way to look at things. It is easy to design an omnidirectional mic. Just have the diaphragm open to the air on one side and seal the back. It is easy to design a figure-of-eight mic. Just have both sides of the diaphragm completely open to the air.
But to design a cardioid or hypercardioid means applying an 'acoustic labyrinth' to the rear of the diaphragm so that it is not completely open but the sound arriving at the rear undergoes changes in amplitude and phase so that when combined with the signal arriving at the front produces the desired pattern.
Cardioid and hypercardioid microphones are therefore more complex than omni and figure-of-eight, and their sound quality suffers because of this.
So for the most accurate recording, you would choose an omnidirectional or figure-of-eight microphone.
Bear in mind that all mics other than omnis suffer from the proximity effect where the bass rises for sources close to the diaphragm.
In practice though, modern cardioid and hypercardioid microphones are very good, and the selection of polar pattern boils down to these simple rules...
Great home recording starts with a great home recording studio. It doesn't need to be expensive if you know how to select the right equipment for your needs.