As someone with an ancestry subscription and also having had DNA tested, the owner of a previously private and now public tree, and also a husband who has tested who does not have a subscription, I can answer some of your queries.
First of all, if you make your tree private, nobody can see it unless you invite them to do so and if you make your tree public, everyone can see it.
If you attach your DNA results to yourself in your public tree, it will show a 7 generation (to 3G grandparents) pedigree view of your tree to all other matches who have a subscription so that you can see if a connection is likely, also a 10 generation list of your ancestral surnames. It will also show them your ethnicity, shared matches, map and locations.
If you attach your DNA results to yourself in a private tree, matches will be able to see your ethnicity and any shared matches with you.
If someone searches for surnames and places, you will come up as a match, also shared ancestor hints will show to other people, though they won't be able to see any details.
Without a subscription, the only information you will be able to see about other matches is their ethnicity and your shared matches, ie 4 to 6 cousins or closer with whom you share a match. You will be able to contact matches through their DNA page, but not through their home page.
So, I think the best advice might be to build your private tree in advance, when your results get back experiment with what you can see of others trees if they remain private, see what you can and can't do without a subscription.
To get the most out of ancestryDNA you need an ancestry subscription, my husband was offered a half price subscription after he sent his DNA off for testing.
Hope this helps
Regards Margaret