A budget of $10k should be more than sufficient to build up very good noise isolation.
Before you commit to anything, you should find out what the existing construction is. Try to get drawings that show the party wall detail. Theoretically they shouldn't be too hard to get your hands on.
If the adjoining unit is vacant, you may be able to perform a test to see how much sound transmits. If the developer/realtor will let you, you can set up a speaker or two on one side, play some music at the loudest volume you would imagine yourself listening, then go next door to see if it's audible.
If you can't hear anything then you have nothing to worry about. If you do hear something, then you can get an idea of how much improvement you would need to build into your unit.
If the developer/realtor really want to sell you the property, they would probably be very happy to accommodate your unusual request. In fact, if you discover that there are deficiencies, you may be able to work the cost of doing sound isolation renovations into the purchase price. Although, being for auction, that may not apply.