BasecampKit is the product of project I was working on a long time ago that never shipped. It should handle all of the networking and models of the Version 1 Basecamp Next API. BasecampKit does not currently handle any authorization/authentication, it assumes that you have access to an account and have passed that account's identifier to BasecampKit.
BasecampKit has two dependencies, AFNetworking and Google's NSString+HTML class. These are included in the libs folder so if you already have them in your project then you should just be able to leave that folder out.
Initializing BasecampKit is as easy calling [[Basecamp sharedCamp] setAccountID:myAccountID];
After the account id is set you should be able to call almost all of the methods described in the header and be returned the appropriate object(s).
BasecampKit is released under the MIT license. Please feel free to ignore the license information in the source, I just haven't gotten around to changing that yet.