The prohibition of purchasing and building applies during the Nine Days, not all of the Three Weeks.[1] Some Acharonim extend the prohibition to the entire Three Weeks, and we try to conform to that practice.[2] However, if it would cause a significant inconvenience or a loss to delay the purchase or building, then one can certainly be lenient.[3]
Regarding what type of building is prohibited, the gemara[4] distinguishes between “building of happiness,” like preparing a home for a wedding, which is forbidden, and preventing a wall from falling, which is permitted. There is a machloket amongst the Rishonim about cases in between these extremes.
The Mishna Berura[5] distinguishes between the needs of a home and beautification or extra, unnecessary improvements. Thus, one should not plan to expand his dining room or paint during the Three Weeks. However, if one started before the Three Weeks and the work dragged on, then he can finish the job if it is difficult to stop in the middle.[6]
It is certainly less of a problem to buy wallpaper than to have it installed because it is the installation that brings happiness.[7] Installation may even require a beracha of Shehecheyanu (there are many customs on the matter), which is forbidden during the Three Weeks.[8]