If you have a PC or Mac, Audacity is a free program you can download. There, you can do basic mixing and editing to your vocals. On Macs, Garageband would be another option. If you don't have a computer, I believe it as an iPhone/iPad app version, though I'm not sure if it's different from the Mac version. There's a more advanced program called Reaper as well. It costs 60$ to permanently use, but there is a 60-day free trial (it is available on both Mac and PC).
There are some apps on iPhone for mixing, though I'm not sure if they can measure up to the computer versions. Djay, Edjing, and Cross DJ are all options, though they do cost money.
If you have a microphone, it would instantly better the quality of the recording. Based on my experience, Blue microphones are good microphones, and a lot of youtaite and utaite seem to use them. Blue snowball mics cost around $50.00. Though it's not the best, a pretty basic mic, the Tonor TN12326 is around 10 to 20 dollars, depending on where you buy it, though it only operates on a PC. These are all operable on computers, as they are USB mics, but there are Bluetooth mics available as well.
On Google+, there is a group of singers called Youtaite World (plus.google.com/u/0/communities/113664509365611168992) that frequently ask each other to collaborate on choruses and such. On Twitter, you can try and find new utaite and PM them, though I'm not sure how to find them (sorry about that).
If you have any more questions, I'd love to help out with them!