Ancestry.com will fit the bill. This is basically how I use it.
I have a paid account, and I've "shared" my tree with a half-dozen or so family members who all have freebie accounts. They can't see the Ancestry paid-only documents that I've attached to people, but they can see the source citations for those documents, as well as all of the vital information, uploaded photos and documents, etc. that I've attached to the people.
You can set your tree on Ancestry as either public or private. Public trees are viewable by any Ancestry member, but living people are anonymized (they can only see the sex and relationship, no names, dates, etc.). Private trees are only visible to you and anyone you specifically share them with.
Regardless whether you go public or private, when you specifically "share" your tree with someone, you can give them one of three roles:
- Guest (read-only)
- Contributor (can edit facts, add photos and documents, etc.)
- Editor (can do the above plus add/remove people)
"Editors" can always see living people, but for Guest and Contributor roles you can decide if you want them to see that information.
Sharing is easy to set up, you enter their email address and Ancestry prompts them to create a free account if they don't have one already.