Well, for small projects  with the following features, traditional SDLC
(waterfall) is the best:
1- Requirements do not change
2- You know the risks and they are small
3- Design is simple

RUP unlike waterfall is iterative but is so heavy and must be
customized and is good for big projects.

RAD mostly uses prototyping and is good when you need to deliver fast.

JAD is good for collaborative projects. You are face to face with
customer.

Agile methods  emphasize on delivery, face-to-face communication but
not much of documents. Most agile teams are located in a single office.

Returning to your question  waterfall is best for small projects that
you know its ups and downs.

If you care about documents go for RUP and if you don't care much then
depending on some other factors you can choose others.

Regarding modification, whatever methodology you choose you will
definitely will modify  it for your needs. Obviously if the project is
small then you do not need to produce a lot of documents related to
waterfall methods.