Well there are a few things you need to worry about.
Contract, yes, this is 100% needed, otherwise you might not get paid. The details of the contract are what might by challenging, especially about how to charge, which is what you're asking.
If you charge an hourly rate, you have to worry about being fair when you charge, and I'm sure the client will worry about this. If you're on the clock, it's not fair to check your email, YouTube, or even Stack Overflow (gasp!). Then there is also the question about whether you should charge if you need to learn some new skill. For example, if you have to learn library A, is this charged to the client or should it be done on your own time?
With a flat rate, you have to worry about keeping yourself productive so that you don't end up with a lower hourly rate. On the other hand, if the job turns out to be easy, you can finish quickly, and end up with a good hourly rate. This probably would be a lot more fair to both parties since no one would be monitoring you so that you're not goofing off and you wouldn't be doing something unethical if you decided to surf the internet while you're working.
If this is a side project and not a long-term job, I'd highly recommend a flat rate. Make sure you estimate it properly though. Take a guess of how many hours you think it will take you, add 20%, and then multiply this by some reasonable hourly rate. The other party will most likely be much more open to a flat rate since then it will be like they are paying for a finished product, rather than a developer.
Good luck!