You do not have to pay anything other than the cost of the electricity in order to set up server software on your own computer. Start with that, learn the fundamentals, then look to progress. I hate to say it, but I think you may be trying to take on too much too quickly.
“[@Michiel:] here in Belgium they let you pay for a whole year at once and that's something I'd rather not do :)”
To be honest, every single country I have ever had dealings with (Netherlands, US, Sweden, all over the place) wants you to pay a year in advance. And personally I wouldn’t trust hosting companies that bill you every $3 bucks separately, monthly.
That is not to say they can’t offer refunds. My current host — Binero — has a money back guarantee that promises me they will refund the months I have left on my account in case of an early termination. You might want to look for similar deals.
People tend to switch hosting once they have learned more. Don’t be afraid to start out with something (very) cheap that seems to offer the right set-up for you. One.com is a hosting provider that comes to mind. Many starting website owners I have come to know here in Sweden use it. They are cheap, fast, and simple. (I haven’t checked it they have what *you* need, but generally, they have.)
But as @Ben says, it is better to set-up a local server on your own computer for testing before doing anything. This way you can learn about NNF and how you want to customise it before paying people for time you need to test things out.
If you do end up looking for hosting I’ll leave you the following tips:
1. Don’t do too much shopping around. If you find a cheaper hosting provider but their website looks more dodgy: don’t take them.
2. Look for a company close to home. This makes it so much easier if you need support as you will be familiar with country customs, holidays, language, etc. Doing business with Japan or Kuwait might not be the smartest move.
3. Test their support. Do they have a telephone number? Maybe call them for information about your first ever hosting deal; Email them some questions about their service and see how fast they answer you back; See if they do support in your own language: this might not seem important but if you ever need something specific in the future it will really make things easier.
4. Make sure they support what you need. Most systems like NoNonsenseForum, CMS, and blogging tools, are developed on Unix machines. Unix (Linux) hosting is often the better choice over IIS (Windows) hosting. For nice URLs (URL Rewrites) you need `.htaccess` and `mod_rewrite` to function and to be accessible. PHP is often a given, *but beware!*
*PHP is tricky* and a lot of hosting companies provide only half the information you need without you asking!
The current version (as of writing) of PHP is `5.4.3`. You want at least `5.4`. The previous version is still around as `5.3.13` but in accordance with the PHP timeline this one is only getting known bugs and security issues fixed and nothing more. From Wikipedia:
“Once per year, a minor release should occur which can include new features. Every minor release should at least have 2 years of security and bug fixes, followed by at least 1 year of only security fixes, for a total of a 3 year release process for every minor release. No new features (unless small and self contained) will be introduced into a minor release during the 3 year release process.”
You will find a lot of hosting companies stating they are running PHP 5. If they tell you this, ask them *what version*. PHP 5.0.0 was released late 2004. That is almost 3 3-year release cycles ago. If they tell you they run 5.3 you can ask them when they are planning to update or just move on and find a new hosting provider.
I hope you’ll take this to heart when you start looking :)
Martijn added on
As Kroc correctly points out  you will be looking for `5.3`, not `5.4`. 5.4 is almost never supported by simple shared hosting providers. I was confused because I am running this version myself and it is the current stable release along with 5.3.
`5.2` is not unheard of, but hosting that provides you with `5.3` is in my opinion much better. As I commented to Kroc:
“doesn't scale well , what do you mean with that ?”
It simply means that NoNonsense Forum probably won't handle a thousand people using it at once :) It's a simple forum designed for no more than a couple of hundred people at a time. Also note that it lacks many features for protecting against abuse (such as banning); so you are expected to handle that yourself. You can choose for example to have an open sub-forum where people can request permission to post, and then lock the other forums so that only registered members can post.
Your friendly neighbourhood moderators:
Kroc, Impressed, theraje, Martijn