Hi,
Unless the SEO issues you are talking about are very serious, I would rather let search engines index the website from the start, to gain time. History is a factor in SEO and, for a new website, it may take time to get noticed by SE.
I mean that Google gives a positive weight to the fact that a website has been out there for a longer time, compared with new website. Moreover, if you implement Google Analytics from the start, you can start optimizing having already some data (vs. having no data at all when you start optimizing).
The only strong case in which it is wrong to index a website is if you thing people should not see it, which does not seem to be your case.
SEO is a process and a game of adaptation.
Wish you good luck.