I suggest returning it and buying something better. Usually dynamic
mics use a 1/4" jack and condensors use an XLR.

No, usually ALL mics have XLR outs. You can use any mic cable you want
to with either mic.

You can easily convert
1/4" to XLR.

Yeah, just swap the radio shack mic cable with a professional one.

They both sound pretty much the same.

Why would the connector on the end of the cable change the sound of the
mic?

Why not spend a
little more and get a decent Behringer or Mackie mixer with built in
preamps?

Why not spend even more and buy an existing professional recording studio?