There are many other threads in AAM that deal with sound proofing.
First of all you need to do a bit of research. Soundproofing is a misnomer as sound travels between 2 houses (sharing a party wall) in more than one way. Sound reduction may be the way to go here. If this seems like semantics (reduction versus proofing) then IMHO it is not as this could affect the design and cost of the solution you require.
In other words, you possibly want noise suppressed to reasonable or tolerable levels, not eliminated altogether. Also you need to resolve how much you are willing to invest in a solution that could become redundant if different tenants move in next door.
We recently had similar decisions to make. We got the builders to apply reduction measures (e.g. rockwool) to alleviate our neighbour's concerns - but not the sound proofing as she was looking for. In a semi-d house, some noise is inevitable.