Для репродукции подобрали матовый багет.

Because для requires the genitive case.

• репродукция = nominative singular
• для репродукции = genitive singular, meaning for the reproduction

So для репродукции literally means for the reproduction.

In this context, репродукция usually means an art reproduction: for example, a printed copy of a painting or image.

So this is not about biological reproduction. It is the kind of reproduction you hang on a wall, often in a frame.

Подобрали is the past tense of подобрать, which means to select, to pick out, or to choose so that it suits something.

That last idea is important: подобрать often means not just choosing randomly, but choosing something that is a good match.

So here it means something like:

• they selected
• they picked out
• they chose a suitable

In context: they picked out a matte frame that suits the reproduction.

In the past tense, Russian verbs agree with the subject in gender/number.

• подобрал = masculine singular
• подобрала = feminine singular
• подобрало = neuter singular
• подобрали = plural

So подобрали tells you the hidden subject is plural, usually something like they or sometimes we, if the context makes that clear.

Russian often leaves the subject unstated when it is understood.

Подобрали is perfective.

Its imperfective partner is подбирали / подбирать.

Here is the difference:

• подбирали = were choosing / used to choose / chose in an ongoing sense
• подобрали = chose / selected, with the result completed

So подобрали presents the action as finished: they successfully selected the frame.

Матовый means matte, non-glossy, or not shiny.

It describes a surface that does not reflect much light.

So матовый багет is a matte frame or frame moulding with a matte finish.

Not here.

Although багет can look like the French word baguette, in Russian it often means picture-frame moulding or simply a frame in art/interior contexts.

So in this sentence, матовый багет is not bread at all. It means the frame or frame moulding chosen for the reproduction.

Because багет is a masculine inanimate noun, and here it is the direct object of подобрали.

For masculine inanimate nouns, the accusative singular looks the same as the nominative singular.

So:

• nominative: матовый багет
• accusative: матовый багет

That is why the form does not change.

Russian word order is flexible, and the beginning of the sentence often shows what the speaker wants to frame as the topic.

Starting with Для репродукции puts the focus on what the frame was chosen for:

• Для репродукции подобрали матовый багет. = For the reproduction, they selected a matte frame.

A more neutral order is also possible:

• Подобрали матовый багет для репродукции.

Both are grammatical. The original just foregrounds for the reproduction.

Yes, depending on context.

Russian past-tense verbs do not show person the way present-tense verbs do. So подобрали by itself only tells you plural, not whether it is:

• they selected
• we selected

Usually context makes it clear. Out of context, English often translates it as they selected.

A fairly literal version would be:

• For the reproduction, they selected a matte frame.

A more natural English translation might be:

• They chose a matte frame for the reproduction.
• They picked out a matte frame for the reproduction.

The exact wording depends on how natural you want the English to sound.