في السوق أذهب إلى متجر قريب، لأن ثمن القميص هناك رخيص.

Starting with في السوق (In the market) is a common way to “set the scene” first. In Arabic, prepositional phrases can be fronted for emphasis or context. You can also say:

• أذهبُ إلى متجرٍ قريبٍ في السوق = I go to a nearby shop in the market.
• أذهبُ في السوق إلى متجرٍ قريبٍ = I go (while in) the market to a nearby shop.
  All are grammatically possible; the choice affects what sounds most natural and what you want to emphasize.

إلى means to (destination). Prepositions in Arabic require the following noun to be in the genitive case (جرّ). So in fully vowelled MSA you’d get:

• إلى متجرٍ (genitive, often shown by -in tanwīn)

In standard Arabic, adjectives typically come after the noun they describe:

• متجرٌ قريبٌ = a nearby shop
  The adjective قريب agrees with متجر in definiteness, gender, number, and case (so with full endings: متجرٍ قريبٍ after إلى).

As written, متجر قريب is indefinite: a nearby shop. To make it definite, you would normally add الـ to both the noun and the adjective:

• المتجرُ القريبُ = the nearby shop
  (And after إلى: إلى المتجرِ القريبِ.)

It’s a nominal sentence (جملة اسمية), very common in Arabic, especially for present-time statements. Instead of saying is, Arabic often omits a present-tense copula:

• ثمنُ القميصِ هناك رخيصٌ = The price of the shirt there is cheap.

ثمن القميص is an iḍāfa (construct phrase) meaning the price of the shirt:

• ثمنُ = price (the “possessed” noun)
• القميصِ = the shirt (the “possessor” noun)
  In iḍāfa: 1) The first noun usually has no ال- (it becomes definite through the second noun if the second is definite).
  2) The second noun is genitive (with full endings: القميصِ).

القميص with الـ means the shirt (a specific shirt, or “the shirt in question”). If you wanted a shirt, you’d use an indefinite form:

• ثمنُ قميصٍ هناك رخيصٌ = The price of a shirt there is cheap.

هناك means there and functions as an adverb of place. It’s flexible in position:

• ثمنُ القميصِ هناك رخيصٌ (there = at that place)
• ثمنُ القميصِ رخيصٌ هناك (also possible)
  The version in the sentence places هناك early to anchor the location before giving the description.

رخيص is describing ثمن (price), not القميص (shirt). Since ثمن is masculine singular, the predicate adjective is masculine singular:

• ثمنُ القميصِ ... رخيصٌ
  If you instead described the shirt, you’d say:
• القميصُ رخيصٌ = The shirt is cheap.

Yes, سعر is very common for “price,” especially everyday price tags. ثمن can sound a bit more formal and can also imply “cost/value.” In many contexts they’re interchangeable:

• لأن سعرَ القميصِ هناك رخيصٌ (or more commonly: منخفضٌ) Note: In very careful style, people often prefer saying the price is low (منخفض) rather than the price is cheap (رخيص)—though رخيص is widely understood.

One common fully vowelled reading is:

• فِي السُّوقِ أَذْهَبُ إِلَى مَتْجَرٍ قَرِيبٍ، لِأَنَّ ثَمَنَ الْقَمِيصِ هُنَاكَ رَخِيصٌ.
  Key points:
• After prepositions: السوقِ / متجرٍ / قريبٍ
• After لأنَّ: the following noun is typically in the accusative: ثمنَ
• Predicate adjective often ends with ـٌ in this kind of nominal sentence: رخيصٌ