There's no need to buy a Robin Hood Hat or RS gold an archer helm: for simple stats checks, the archer helm provides superior defense, however the robin hat provides more defense with a range. It's up to you, the differences are small. Robins work great as a cosmetic item and can be customized to earn loyalty points at Xuan in burthorpe or Varrock, although.
If you don't have them, then you should get some barrow's gloves: They're extremely effective for the glove slot and are extremely useful as a result. It is also recommended to purchase the ranging boots It is recommended to purchase snakeskin because ranger boots (12M) do not fit into your budget.
The shield slot is likely to be a god-illuminated book. Zamorak's book is priced at an outrageous 22 million the better option cheap OSRS gold is armadyl's legal book with a price of 1.7M It's got 2 less ranged offensives, however, it has defense capabilities. Once you've illuminated it you'll get a nice big prayer bonus.