I only know a teensy tiny little bit, people usually record with audacity, then use one of the various mixing programs to mix into the off vocal song with effects and what not.
A decent mic is all that's needed, I think good recording technique such as distance from microphone, and minimising background noise makes up the bulk of recording quality.
You two probably already know, but I listen to lots of broadcasters, and I've seen people with cheap desktop mics sound excellent, it's all about the technique!
For recommendations, I have the Blue Snowball and its okayyy, I'd look into one of them USB condenser mic's (like my Snowball and Lily's Blue Yeti), because getting a proper mic + seperate USB preamp can get a liiiittle pricey/complicated, though it'll be better quality.
But we should let Lily chime in, she's a pro.
I fell asleep while skyping with my imouto once, then I got teased allll daaayyy about snoring. She falls asleep during a call often, I secretly fire up the rig and listen intently. I can think of no greater use for a high end headphone system.
Lily reminds me of Lily (niconico/doujin artist), I have her first CD, and an autograph. I wonder how she's doing now...
One of my favourite covers by her;