To welcome someone into your home you would use the word
benvenuto [ben-veh-nu-to] for a single male guest,
benvenuta to a single female guest, and
benvenuti when welcoming more than one guest, irrespective of gender.
There are a number of ways to refer to your 'home' in Italian, with the most common being the word 'casa' [caz-ah]. Coupled with the pronoun
nostra which is the equivalent of 'our', you'll be able to give a warm Italian welcome to someone by saying
benvenuto alla nostra casa.
In this sentence, the article
alla can also be replaced by the preposition
nella.
Another modification you might hear is the pronoun
nostra working behind the noun, as in
benvenuto a casa nostra.
Obviously you can replace the word
casa for any other reference to your home, from
appartamento (apartment) through to
posto (place).