Learn Spanish (Latin America): Busco un anuncio que tenga la casa ideal. - I am looking for an ad that has the ideal house.

Because the speaker is looking for an ad that might not even exist yet. When you describe an unknown or indefinite thing you are looking for (using words like un anuncio instead of el anuncio), the verb that describes it must be in the subjunctive. If the speaker knew exactly which ad they were talking about, they would use the indicative tiene.

Why isn't there a word for 'for' after Busco?

The verb buscar means 'to look for' or 'to search for' all by itself. English speakers often want to add por or para after it, but in Spanish you just connect the verb directly to the thing you are seeking: busco un anuncio.

Why does ideal come after casa instead of before it?

In Spanish, descriptive adjectives like ideal almost always come after the noun they describe. While English says 'the ideal house', Spanish structures it as 'the house ideal' (la casa ideal).

Could I use publicidad instead of anuncio here?

Not quite. Publicidad refers to 'advertising' as a general concept or industry. Since you are looking for one specific listing or classified ad, un anuncio is the correct word to use.