Can it be written entirely by myself (never got legal training) following the examples of my competitors? If not, is it worth writing it myself and then asking a lawyer to review?
If your needs are not too complex, and relatively standard - what I would recommend is trying out Trust Guard's generators to walk you through creating both documents.
Privacy Policy Generator
https://www.freeprivacypolicy.com/
Terms of Service Generator
http://www.termsofservicegenerator.com/
They are relatively in-depth and cover most situations, unless you're like Facebook. Then you would need an attorney.