Verbal agreements can make the best of friends enemies very quickly. If it is a true business person on the other end, they will respect having a written contract.

As to your fees, do a comparative analysis of the market, subtract 15 - 20% off of the average (obtained by tossing out the highest and lowest and averaging the rest) to compensate for your lack of "title".

In the future, since you have experience, if you plan to do this again, do not undercut your fees, simply charge on the low end until you have done 5 - 10 jobs, at which point, begin to steady increase your fees per project until you reach the amount competitive with the top 25%.

Congratulations on such a rewarding project!