I wouldn't wish the Little Liddell on my worst enemy. For the cost and the help it gives, your best investment is probably the Middle Liddell, as long as you always consult up-to-date scholarship and annotate it as you go. The Great Scott isn't worth the cost considering all of the errors and omissions.
For example, you'll come across a fragment of Anacreon and wonder what a smith is doing beating bronze with an axe (πέλακυς). A good commentator will point you to a 70-year old article in a German journal asking, "axe, or hammer?," and soon it's clear that the word here (and elsewhere) means hammer (i.e."striker;" see ahead) and is not derived, as LSJ claims, from a Babylonian loanword, but is an augmented form of P.I.E. *pel-, "to strike" (which, incidentally, is the root in English anvil).
In fact, many definitions in the LSJ are based on disputed readings that have since been completely rejected. It can be a struggle, which is why I think historical and comparative linguistics is so helpful.
As you progress you'd do well to consult author specific lexicons like Slater's Pindar (helpful with a lot of lyric), or even Autenrieth's Homer.