Answer: esta
This sentence is a good example of the usage of the demonstrative adjectives in Spanish.
These type of adjectives are those words that accompany the noun to mark the distance that separates the speaker from the object, place or person to which they refer.
They agree in gender and number with the noun they modify, and (similar to English) they are generally written before the noun it modifies.
The three demonstrative adjectives are:
Este (This): It describes a noun that is close to the speaker and the listener.
Ese (That): It points out nouns that are further from the speaker and not easily reachable. The noun may be close to the listener, but not the speaker.
Aquel (That over there): It is referred to nouns that are far away from both the speaker and the listener.
Each one has four different forms that vary by gender and number, and they are listed below:
Este
Masculine Singular: Este (This)
Feminine Singular: Esta (This)
Masculine Plural: Estos (These)
Feminine Plural: Estas (These)
Ese
Masculine Singular: Ese (That)
Feminine Singular: Esa (That)
Masculine Plural: Esos (Those)
Feminine Plural: Esas (Those)
Aquel
Masculine Singular: Aquel (That over there)
Feminine Singular: Aquella (That over there)
Masculine Plural: Aquellos (Those over there)
Feminine Plural: Aquellas (Those over there)
Now, in the sentence canasta (basket) is a feminine singular noun, in addition we are told to use this. In this case the correct form that matches in gender and number with canasta is esta.
Therefore the sentence is:
Voy a comprar esta canasta vieja
I'm going to buy this old basket