Hello, Ultranewbie! Welcome to the board! Your question is simple, but your problem is not. I can recommend bizzillions of pieces of relatively simple equipment that will do what you want. You don't need a bunch of tracks, 4-8 is plenty. You also don't need million-dollar pro studio quality. You need a good vocal mic, and an all-in-one multitrack recorder with a CD burner. That will accept inputs from a CD player for your music, and you will need a good cheap vocal mic, say Sennheiser e835.
Now the real problem- Recording equipment, whether cheap or expensive, is designed to capture sound, not make it go away. The better the equipment is, the more sound (noise) it captures. There is no recording equipment that will make a noisy room quiet. Often this problem is addressed by placing a not so sensitive mic (such as the Sennheiser above- a dynamic stage mic as opposed to a studio condenser) very close to the source. That is to say, right in front of the mouth of the singer/speaker. Therefore, the mic will be "in your face". Then you can turn down the input gain and pick up less of the room noise. The farther away from you and the more sensitive the mic is, the more ambient (room) noise it's going to pick up. There is no getting around that reality.
You need to make your room quieter. Start with heavy drapes. Identify the sources of noise, and eliminate or mitigate them where possible. This is done on a case by case basis. No one can tell you what to do about ambient noise without knowing what the noise is, and how it's getting to your mic. Post up some pictures of your room and explain exactly what noises you are hearing on the tape that you would like to decrease or get rid of. The recorder is easy. Four to 8 track recorders with CD burners can be eaisily had in the 500-600 range. A mic will set you back about $100. You will need a mic stand and a good mic cable. That's all you really need. None of that will make noise go away- good luck.-Richie
