This Post Is Obsolete. But Wait. Although 'Basecamp Personal' no longer exists, use Basecamp3 instead in the same way described below. You get one free project. Unlimited members. When this gets hard to manage, the paid account is now just $29/mo for unlimited projects. Or stay free by using Trello™.
'Basecamp Personal' is a scaled-down version of the full Basecamp web application created by 37signals. The main differences with the full version are that you only have one project, you are limited to 5 users, and you only pay a one-time charge of $25. All the other Basecamp versions have monthly subscriptions, multiple projects and unlimited users. Currently you have to be a Basecamp user to purchase Basecamp Personal, but it seems as though 37signals plans to remove this restriction. If you aren't a user now, I think you will be able to get Basecamp Personal soon.
Our project ID convention is to use 3-4 letters in "stock call letter format" (you know AAPL for Apple) to represent the client's name. This is followed by a dash and another 3-4 letters that represent the initial letters of the project name, e.g. FAX = Fine Arts Expansion. (We used an 'X' here instead of an 'E' ... just because.)
The upshot is that we have have most of the benefits of Basecamp for just a one-time cost of $25. Keep your fingers crossed that 37signals opens up the availability to the public.