1) The popular choice for mid-size communities is the obvious one you're on right now-- vBulletin running PHP and mySQL. Sitepoint runs it. I run it (220 peak concurrent). Larger forums run it (Somethingawful.com, 600+ peak concurrent). Get started with the vBLite version or phpBB if you want to avoid the $99. Luckily PHP and mySQL are both free so the startup cost is low.
Anything bigger than that and you are probably going to have to write your own database layer and tie vB into Sybase / Oracle. Or look to a higher-traffic community like Web Crossings (CNN, ESPN). Here you're talking about server farms and 10's of thousands in licensing fees if not more.
2) Read Sitepoint's hosting forum for the latest info. Also check vBulletin.com's host forum. Both will have many hosting options and lots of opinions on a suitable site for a community vB. I'm sure SP wouldn't mind if you clicked their new hosting sponsor to check prices as well.
I don't really know the particulars about Snitz Forums but from what I do know they have scalability built. More than even vBulletin does currently.
Right now you have MS-Access as a backend. You can probably support up to 20-30 concurrents with this software. That can be 300 posts a day. However if you are going to grow like you hope you can hit this ceiling quickly.
Snitz also works with both MySQL and MS-SQL. Your next step up would be MySQL. This as Overgrow said can be scaled to over 600 concurrent users with the proper server environment. Not all servers will be capable of this.
Your final choice is MS-SQL Server. This is a medium to large scale enterprise class database server and it is offered by many Windows hosting plans. It may even be offered by your current host as an account add-on. Upgrading from Access to MS-SQL Server is relatively easy and Microsoft distributes an upgrade tool to make it easier. This server is designed to handle 1,000s of concurrent users over multiple machines. In my opinion there is only one database system that is more scalable than this and that is Oracle. Alta Vista used MS-SQL Server exclusively for their search engine up until recently. They get millions of uniques a month.
Check on the Snitz support forums and see what the members there have to say.