I don't believe the paid forums like vbulletin or simple machines are any better or more reliable than open source forums like phpbb or punbb. Any traffic problems down the road will be more likely related to hosting than the forum scripts themselves.
Often when hosting companies offer free scripts, they are simply open source scripts that you can get anyway. I would recommend getting and installing a forum yourself without using a hosting companys' installer so you're getting the most up to date, stable version.
I'm not familiar with Hostway, but a lot of hosts prevent scripts from creating databases, so you go to the hosting control panel, then phpmyadministration and create your database. You don't need to create any db tables or anything else, just the database itself. Once created, you'll have the necessary info for the database, (host name, database name, mysql user name and password). Sometimes you have to append a port number to the database host name. Your host should help you with this.
Upload all the necessary files for whichever forum you chose. Some might require you to edit a configuration file first with the above mentioned info.
Once done, point your browser to the install file and follow the prompts, fill out the form, whatever.
Once done, delete the install file from the server and you should be good to go.