Basic beliefs (sometimes called foundational or core beliefs) involve ultimate authorities. They are built on the ground-floor assumptions that form the foundation for your worldview. Those who believe human reason is the ultimate authority must use it to defend their arguments for rationalism.
Those who believe sense-experience is the ultimate authority must presuppose it in their defense of empiricism. Those who believe skepticism is the reigning authority must subject their own philosophy to the same standard of skepticism.
The only arguments for basic beliefs are circular. It's true that circular arguments are not usually convincing (even when the premises are true and the conclusion is valid). But there is a difference between narrow (vicious) circularity and broad (virtuous) circularity.
Vicious circularity assumes its stance rather than providing evidence for it. It avoids the burden of proof, and it often restates the conclusion in one of its premises. But not all circular arguments involve vicious circularity (aka "begging the question").
Virtuous circularity occurs when you consistently apply the fundamental principles of your worldview to your method of collecting evidence, evaluating arguments, drawing conclusions, and (most importantly) accepting the consequences of those conclusions.
John Frame calls this "circular coherence". This kind of circular reasoning is only legitimate when it is used to explain or debate the ultimate criterion for a system of thought or the reliability of our cognitive faculties.
As finite creatures, this is the only option available to us. We must go round and round an idea to understand it. Unless of course we are larger than the thing we're investigating.