A simple cost-benefit analysis will probably point towards a template-based, customized framework.
From client-side considerations like design, user experience, cross-browser and cross-form factor testing to back-end concerns like storage, cross-domain validations, authentication and security - and these two lists are way, way far from being comprehensive - I'd say that a template will save you a lot of time and frustration.
Would it matter if I coded my own website from scratch or just worked off of a template?
Since you're a data scientist as a potential employer I would be looking at your training or your expertise with core competencies like machine learning, R or Scala; a good design would play a minor role.
are there any preferred websites out there which make it reasonably simple to edit the code (e.g., Squarespace, Wix)?
Both services mentioned offer fairly simple to use editing interfaces.