According to Chris Giles writing in the Financial Times a few days ago, "Economics cannot tell you what the right level of government debt is..." Well Modern Monetary Theory (MMT) can. I'll explain.
MMT (and indeed Positive Money) advocate that in a recession, government should simply create new money and spend it, and/or cut taxes. And it should carry on doing that until the recession has ended.
One reason that policy will eventually cure a recession is that a deficit increases the so called "national debt," and that debt is an ASSET as viewed by the private sector (which holds the debt). And the more paper assets of that sort that the private sector holds, the more it will spend. Thus (roll of drums) the "right level of government debt" is the level that induces the private sector to spend at a rate that brings full employment (aka brings the end of a recession). And that right level is brought about by the latter policy - or to be more accurate, under the latter policy, the debt will always be moving towards the right level.
As to what rate of interest government ought to pay on that debt, that (as MMTers keep pointing out) is entirely under the control of government - at least it is in a country which issues its own currency. At the extreme, government can perfectly well print money and buy back the entire debt, in which case government would be paying zero interest on the so called "debt.". In fact the debt would turn into cash. Indeed we've been doing pretty much just that for the last five years under the guise of QE. And as for the idea that money printing causes inflation, well, where's the inflation that QE was supposed to cause when it was first mooted? Nowhere to be seen.
And a zero debt regime is not such a daft idea: Milton Friedman and Warren Mosler advocated the idea. An alternative is an ultra-low interest rate debt (e.g. the 0.5% or so that they have in Japan). The merit of that is that it's not so easy for the private sector to spend bonds as it is to spend cash, thus the chance of a sudden spike in spending with a consequent rise in inflation is reduced.
Having said that QE has not caused inflation so far, that's not to say a large scale and continuous QE program it MIGHT NOT do so. But if that happens, there are a number of deflationary countermeasures government can take. 1, raise taxes. 2, cut public spending. 3, raise interest rates.
As regards raising interest rates, it would not be possible to do that via conventional means, i.e. keeping commercial banks short of reserves (aka base money). Reason is there'd be too much base money (i.e. reserves) sloshing around. However, the central bank can always pay interest on reserves, or raise banks' minimum reserve ratio (while paying no interest on such reserves). The latter strategy seems to be much more common in China than in the West.