Today’s topic is an adversative conjunction, [てform]+も, which is usually translated as “even if”.
All of the above choices include an adversative conjunction (a conjunction that connects contrasting/opposite parts) but in this example only d. たかくても can be used.
あのレコードがあったら、高くても買います means “If (a shop) has that record, I will buy it even if it’s expensive.” In this situation, the record being expensive is only an assumption, not a fact, because あのレコードがあったら suggests that they (shop) may not have it, and [てform]+も is the only one here which can be used with an assumption.
Some more examples of similar use:
Even if it rains, I will run 10 km.
Even if you look for it, you won’t find it.
It can’t be helped even if it is not found.
I’ll do my best even if it is difficult.
I’ll eat it even if it is not delicious.
さしみは しんせんでも たべない。
Even if sashimi is fresh, I won’t eat it.
It is OK even if he is not studious.
If the sentence did not have あのレコードがあったら, all other 3 sentences make sense and they mean:
a. たかいが 買（か）います。It is expensive but I will buy it.
b. たかいけど 買（か）います。Although it is expensive, I will buy it (almost the same with the above)
c. たかいのに 買（か）います。Even though it is expensive, I will buy it. (not much difference from the above 2)