No singer is without a good quality Microphone.
The classic vocal mic is the Shure SM58 series. They're durable, sound great, and will take anything you throw at it. If you're recording, you want to pick up a condenser mic, because they're much more dynamic, which means they'll pick up all the little details.
Condenser mics are usually more expensive, but they're worth every penny. Quality condenser microphones are manufactured Rode, AKG & Sennheiser.
Make sure you put them through a decent preamp so you can get the full dynamic range when you're recording vocals or guitar.
Check out prices for new & used microphones below.
SHURE SUPER 55 DELUXE VOCAL MICROPHONE S...
SHURE SM58S DYNAMIC MIC W SWITCH + XLR + ST
SHURE SM7B RADIO TV DYNAMIC VOCAL MICROP...
SHURE ULXP4 BETA 58 PRO WIRELESS MIC SYSTEM
SHURE BLX24 SM58 HHELD WIRELESS VOCAL MI...
SHURE SM58S VOCAL MICROPHONE WITH ON OFF SWITCH
SHURE BETA 58A HHELD DYNAMIC VOCAL MICROPHONE
SHURE KSM8 DUALDYNE DYNAMIC HHELD VOCAL ...