After #moccamonica 's question about buying advice for a good recording solution I decided to share my thoughts on the subject.
First of all the recording quality of any recorded music depends on your budget. On the money you have invested either in equipment or in your education on recording.
Lets overlook the education part (while it is the most important!) and focus on the equipment you might get.
The fast and easy solution:
There are many portable field recorders made by Tascam, Zoom, Roland etc. which usually have two small diaphragm condenser microphones arranged in a xy pattern. The device is capable of recording many channels of music and probably has some editing functions. This is the easier way to record music with quality better than your mobile phone. I would prefer Tascam or Roland as I believe their quality has always been over certain standards.
2. The medium solution:
If you own a pc or laptop you ca get a usb microphone and connect directly to a usb port. The advantages of this solution is that you can edit your music inside a DAW (like Cubase) and you will eventually have better editing capabilities than with a field recorder. You can also get a large diaphragm condenser microphone, which usually have better quality than small diaphragm ones. In case you think of the DAW cost, most audio equipment nowadays comes with bundled DAW software, so that probably won't be a problem. I would look for good microphone manufacturers like Blue, Rode, AKG and I would stay away from new emerging chinese companies.
3. The hard and pricey solution:
In this scenario, you must get a good condenser microphone, a good mic preamp and an audio interface that will eventually get your sound into the digital universe of the DAW. Most people just use the standard preamps of their audio interface and don't get a separate mic preamp. So, for microphones I would still go for Rode or AKG and I would suggest a cheap audio interface with a separate good mic preamp. Since this solution gets kinda out of any standard budget, I could also suggest a decent audio interface.
But, why a cheap and not a good audio interface??? Well, I used to own a Digidesign audio interface, a Focusrite Scarlett and now a Yamaha AG03. From this little experience I say that cheap stuff is always cheap stuff. It doesn't matter if it's labeled Focusrite or Neve or anything. So, if you want quality you must buy a separate mic preamp preferably with a digital output and any audio interface with a digital input supporting at least 24bit/96kHz. Even better are the hardware channel strips which offer more a compressor, a noise gate and an eq.
I also owned a Presonus Tube-PRE as a cheap preamp, which proved a total waste of money as tubes are good, but they need high voltages which won't happen with an 18V power supply :)
Of course if anyone wants to get involved in the labyrinth of the 3rd solution a great way to cut down the cost is to look for 2nd hand equipment. At least a 2nd hand soundcard can be sold again at almost the same price if it is not satisfying. And Focusrite platinum vocal series are sold really cheap nowadays...