What forum would anyone recommend to use?

A client of mine is asking me to add a forum to one of his WordPress websites that I’ve built for him. The website is built with a child theme of Genesis.

I was originally looking at phpBB and then while looking at the list of forums that I can install using the Softaculous package, I noticed bbPress (which I then noticed was from the creators of WordPress). So, naturally, I decided to ask the WP experts for an opinion.

1) Would you recommend that I use bbPress?

2) What pitfalls can I expect when installing the suggested forum software?

3) Can the suggested forum software emulate my theme that I used on his website?

4) Any other suggestions/warnings would be appreciated.

Thanks in advance.