Learn Swedish: Jag gillar bläcket du valde.

In Swedish, just like in English, you can leave out the relative pronoun som (that/which) when it is the object of the relative clause. Because du (you) is the subject doing the choosing, som can be safely dropped. You could perfectly well say Jag gillar bläcket som du valde, but dropping it is very natural in everyday speech.

Why do we use the definite form bläcket here instead of the base form bläck?

When a noun is followed by a relative clause that specifies exactly which thing we mean, Swedish uses the definite form. This matches the English translation "the ink you chose" rather than just "ink". Bläck is an ett-word, so it takes the -et suffix to become definite.

Valde is in the past tense, but what is the infinitive form of this verb?

The infinitive is välja (to choose). It is an irregular verb that changes its root vowel and drops the letter 'j' in the past tense. The principal parts to remember are väljer (present), valde (past), and valt (supine).