Depending on the potential niche audience and estimated forum traffic, having a good web host is a must for launching your forum. Personally I use Host Gator and find their support and pricing seems to be the best around. You can pick a plan here - but for the $6.95 per month I would take the unlimited plan and also purchase a dedicated IP address. Having the dedicated IP will make setting up your Domain Name DNS and or just pointing the domain to your hosting account easier. Forums like vBulletin and other popular software run off of MySQL databases. So with a Host Gator hosting plan, having cPanel to easily set up the databases and create your email addresses makes life easy.
As your forum grows you will want to understand a few important things. First, hosting a popular forum loaded up with photos, avatars, and some mods can slow down your sites load time. Imagine several hundred or thousand people on your forum all reading, posting, and uploading pictures at the same time. It can become demanding for a minimal shared hosting account and your forum will start to slow down and perform poorly. At some point in the future when your forum reaches a certain level of traffic and posting per day, you will want to look into a dedicated hosting plan. Additionally, in time you could find yourself running a forum with multiple servers, one for the presentation, one for the MySQL database, and maybe a third to host images or your ad server. Scaling your hosting will become a topic down the road if you are successful at growing your forum. Hey, this would be a good problem! I just wanted to mention it now so that when the time comes it will have been something that you were aware of.