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.[1]
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.
[1] 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.