The first question to ask is Does the word "basically" add any meaning or value to the sentence? For me, the answer is a definite No. The best position for basically in that sentence is the garbage can. If the word were only, however, the question would have some meaning. Modifying Merk's example sentences:
"I'm only searching for conversation classes."
"I'm searching only for conversation classes."
gives two sentences that most native speakers would agree mean the same thing and are merely style options.
It can come at the end of the sentence:
"I'm searching for conversation classes only."
in which case, it means the same thing as the first two.
If it comes at the beginning:
"Only, I'm searching for conversation classes."
the meaning of "only" changes to "except" or "but", as in:
(A) "I see that you're wasting time surfing the Internet again."
(B) [Nods head in affirmation and says:] "Only, I'm searching for conversation classes."
I don't know whether this usage is universal or just part of my dialect, however.
 I don't agree with that because I think the continuations are logically different, but that's a different discussion and the answer to a different question, so I won't get into it here and will say only that, for the sake of argument and this question, I'll accept what most native English speakers would agree to.