A few drops of hydrogen peroxide will not hurt, and it can actually help to keep the nitric from decomposing as NO2 gas,.
The thick brown HDPE bottle will work for storage for short term, but if your thinking of storing for long term then use glass (protect from light), also the concentration of the nitric acid should be a consideration when storing. when storing nitric the nitric can decompose to NO2 which can build pressure in a container, dilute or clean solutions would decompose less than highly concentrated or solutions with other things like metals in solution, storage temperatures and light conditions can play a major role in storage, bottle caps are important, even the glass bottles I buy nitric in after a period of time the caps will break down and become brittle, sometimes breaking, I feel nitric acid is just better not stored long if you can help it, remember do not store your nitric where an accident could occur, keep from strong bases and organics, a catch basin and a place where if fumes did escape they would not cause damage, out of reach of children and animals, not in your house or workshop.