No, you don't need to worry about hyperinflation, the big bugaboo of Chicago/Austrian economists. Hyperinflation is associated with economic collapses like wars or industry failures, where suddenly goods are in short supply. What you get out of this is ordinary inflation, not hyperinflation. If you print 1% of your economy in new money, then you get 1% inflation. Hyperinflation is a different problem.
Ordinary inflation can be dealt with in a number of ways. Taxes are one of them: you don't pay down the debt but just burn the money. You don't need a separate account book for government debt: outstanding currency is government debt.
Not all economists buy this theory. It's not mainstream, but neither is it exactly fringe. I bring it up only because the notion of a separate government account book that has to be balanced is worth reconsidering. Ditch it, and there are tradeoffs that might be worth it -- including simplifying how you handle basic income.