I don't think you should assume the creeking noises come from the tile. At any rate 15 year old tile is probably kind of out-of-style if it's vinyl tile. You never say whether it's vinyl or ceramic, or other.
If it is vinyl tile the best job would be to remove it, although I've seen jobs where it's been added to the top of original and has worked okay. Using a good adhesive and locking in the job by either removing and reinstalling the baseboards, or, adding a piece of one-quarter round along the bottom edge of the baseboard, rolling it and then sealing the installation with a hi-quality wax can help make it last.
The tile for 1000 sf ranges from $.72 a sf to whatever you want to pay. Prices in a 2006 costbook I have show labor at $ .70 a sf. The same costbook shows removing the tile at $1.73 a SqYard. That doesn't include hauling, dump fees, etc.
If the tile is ceramic then labor and installation is probably close to starting at $6 a SF with removal at $6.50 a SY. Again, no hauling or dump fees.
There is one caution here and that is that older vinyl tile (70s era but some also later as supplies were being used up by being sold cheaply) can have asbestos in it and the mastic that holds it down can have asbestos also. It's not harmful in place, it's just a problem if it gets dusty and airborne. Still, you should be aware of that.
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