Forum Script - (Usually free with hosting, Phpbb is free) If not VBulletin is like $50 a year.
I'd actually advise against both. phpBB, while is free, also has a very bad reputation for very nasty security issues.
vBulletin, is what the NHC is powered by, and it does a decent job, the cost is a major factor. It is actually $100 per year for a Leased license, which permits one year of upgrades, and $180 for an owned licence which still provides one year of upgrades which will be available at $40 after the first year and within 60 days of the licence expiring), the difference is that with an owned licence you can keep the forum running after the licence has expired while with a leased one you can not.
For the best solution though, I would say SMF, at
http://simplemachines.org, and not because I work for them as a staff member. They have the most customisable template system, it's easy to install and configure, and comes with loads of features as standard and can easily be modded with our Package Manager. It also has the best known security out of the top five BB scripts (phpBB, MyBB, SMF, vB and IPB), just look on any security website. And all for the low, low price of zero dollars.
Of course, I cant tell you which one you should go with, so when you do decide to expand outwards into your own host, and STILL want a forum, play with all the solutions you have available to you, and see which one you like best.