Best Facebook Ads strategy for growth?

Background: I had a personal profile with just under 5000 friends, but which was receiving very high engagement (around 400 likes per post). I've now transferred that profile over to a page and I can sense that the reach (and therefore the engagement) has fallen considerably.

Options: I have no issue spending on Facebook Ads to consolidate the page's performance. My thinking is if I spend money on advertising my posts to those who now like the page (and who were previously my 'friends' on the personal profile), they will engage with it and the reach will ultimately get back up. Does that sound like valid logic?

On the other hand, in terms of getting new engaged 'likers' what's the best way to proceed through FB Ads? Boost page or the posts? Or something else altogether? As mentioned, have no problem spending, but want results and sustainable growth and engagement.

Help would be appreciated.

I would recommend boosting mostly posts and not the page itself because if you work hard enough on one post and making it reach as much people as possible will definitely help you with both page & posts engagements. Posting something that will make people comment and share it with their friends is what you need (Funny, interesting, inspiring posts etc..)
Good luck!