This is year 3 and product is selling good enough. Now we need to
enforce good software development practices.
You are not sure of the quality of the processes and the product and it is still selling? Lucky! No. i didn't want to really criticize you, but my point is that, the fact that your product is doing ok in market, it is a positive sign. Don't throw away things yet!
What you, need really is to slowly make things formal. In my opinion, it is not important to do best fit with respect to some standard process; rather you need to use that suits the team.
I am not very much aware how much maturity you have got in some of this, but make it really work for the team. First of all, you must ensure 4 essential things: a. Version control, b. Bug tracking and c. effective release management. d. Build the suit of regression tests.
In the answer here - i have enumerated some good and simple practices, if followed builds good momentum in the people and it helps bring trustworthy code as the key focus.
The same small step-by-step improvement criteria applies if you want to automate the testing process and move towards continuous integration - start with what most people agree that can be trivially and reliably automated (after a while people will begin to think, why did we ever did this manually).
Finally, about the documentation and code review process. I guess, most programmers wants to do a good job at this one; Issue is there are no consensus, best is try to bring purely a peer driven approach to a larger question: what do all of us think is a good code and documentation! (read this) As you evolve, again people will slowly convert into more of a personal responsibility than policy dodging activity.
This truth is, there are no great alternatives to "small-step-by-step" way of evolving code. Call it TDD, agile, iterative or whatever; these steps is what make it possible that team can fathom the evolution of the code and in all likelihood, try to accelerate to their maximum speed.
Once, people see success in these small steps, and finds the ownership, their biggest commitment to learn better practices and improving even further rapidly increase - leave them with this ownership and you will see wonders!