First of all, you seem like a great friend! Second, what does this guy have already? Is he recording on a computer with software, or is he just using a phone?

Something to keep in mind is that most of the time "nicer" mics are actually more sensitive than cheaper alternatives. So if background noise is already present, it may just end up louder with better gear. However, there are some ways to address this:

1. A directional, dynamic mic instead of a condenser. A solid, inexpensive option would be the Shure SM58. This is one of the most versatile workhorses in the industry. A similar option would be the Audio-Technica ATR2100x-USB. A neat thing about this one is that it gives the option of using either a traditional XLR cable or USB. That would allow your friend to plug directly into a computer and potentially forgo the need for an audio interface. But the audio quality will take a hit. A downside is that dynamic mics generally require more gain than condensers, so he'll actually need a pre-amp or audio interface (depending on his current computer situation) to boost the signal enough to be usable.
2. A vocal shield like this could definitely help too.

If your friend has a Mac, he has Garage Band. Otherwise, he could download Audacity for free which is more than powerful enough for home studio recording. He should get an audio interface of some kind. The PreSonus Studio 24c is a great little interface that comes with software. Another really popular option is the Focusrite Scarlet 2i2 which often can be bought as a bundle with headphones, cables, etc... but the included mics are NOT dynamic and will pickup more of that background noise.

On top of all this, sound will generally come out of the computer, into the audio interface- so unless he wants to only use headphones, monitors of some kind are a necessity. I'm a big fan of the PreSonus Eris 3.5s. I really don't think they can be beaten for the price.

Obviously, the price of gear adds up quickly, so keep your eye out for home studio bundle deals on Amazon, or Sweetwater- which is my favorite gear source. They have amazing customer service/support and in fact, would be happy to answer any of your questions about this stuff.