The word 'but' is a connector to join sentences in a compound sentence. The word 'though'' is a replacement of 'although' to make a complex sentence

We use 'but' and 'though as conjunctions to introduce contrast. Here you have two sentences so the second can only start with 'but'. 'But' can be used in a following sentence to emphasis contrast with the previous one. 'Though' can only be used at the beginning of a sentence when it introduces the first clause. 'Though they knew the war was lost, they continued to fight.' Otherwise if there was a comma after college, I think both would work.