Just forget about "competitors stealing your unique ideas". Really, forget it. You are giving your own brilliance too much credit. You don't even have customers

Just forget about "competitors stealing your unique ideas". Really, forget it. You are giving your own brilliance too much credit. You don't even have customers validating your unique ideas and you expect competitors to take them seriously? So a part from that, regarding your question. A "private" beta doesn't implicitly means "no PR"? A private beta isn't open for anyone to sign up, if it isn't open, why the press should cover it? You gain nothing. But, even if it is not actually "private", I still would suggest "no PR". Launch quietly, let some users come, test, validate your ideas. You will know what to improve and which of your ideas are actually unique. Then you will know what to say when you decide to go with PR. Yes, it means fewer users trying it out and validating. But users that come from press usually are not of the "early adopters" type (meaning: they will be frustrated by the smallest bug, lack of feature or unpolished design and will leave before even trying, leaving no feedback behind). So launch it ASAP, forget press, and submit to places like Show HN, Product Hunt, Reddit, etc.