There is more than one kind of logic. Besides classical logic there are also, for example, paraconsistent logics, modal logics and intuitionistic logics. That means we have choices available to us of which logic to use for any particular class of statements. The question of justifying logic can be rephrased, to emphasize the importance of the task, as justifying which logic to use for a particular class of statements.
Michael Dummett makes a distinction between realist and anti-realist positions regarding particular classes of metaphysical statements, such as mathematical statements, ethical statements, statements about the past or the future to name a few. Furthermore he notes that circularity is not acceptable: (page 8)
The realist thesis is not a possible object of discovery alongside the propositions it proposes to interpret: it is a doctrine concerning the status of those propositions.
This doctrine involves a principle of logic: (page 9)
It is difficult to avoid noticing that a common characteristic of realist doctrines is an insistence on the principle of bivalence - that every proposition, of the kind under dispute, is determinately either true or false. Because, for the realist, statements about physical reality do not owe their truth-value to our observing that they hold, nor mathematical statements their truth-value to our proving or disproving them, but in both cases the statements' truth-value is owed to a reality that exists independently of our knowledge of it, these statements are true or false according as they agree or not with that reality.
Taking a realist or anti-realist position amounts to taking a position on a logical principle with respect to a specific class of statements. Hence justifying the logic we use involves justifying a metaphysical position about that particular class of statements. Since the realist thesis is not justified "alongside the propositions it proposes to interpret" it would require other informal arguments or a logic more neutral than the one being used with the class of statements.
The OP asks:
Can we justify logic in a way that is not circular? Is a circular justification a bad thing?
One cannot use the logic used to study a class of metaphysical statements if the logic itself is ultimately being questioned. Hence an informal argument or a more neutral logic would be needed.
Dummett, Michael, The Logical Basis of Metaphysics, 1991, Harvard University Press.