We just set up a body of our new SW development company. The design of the processes is currently the task concerning us.
We would like to be agile and also to achieve the maturity CMMI Level 3 ASAP.
What would you recommend? How should we begin?
Let me start by saying that, contrary to popular belief, CMMI and Agile go together like "peas and carrots." Since your writing from outside the USA, that's my own way of saying that they are just meant to go together.
Remember, while "Agile" describes "how" you build software, the CMMI only describes "what" needs to be done. There is no reason to think the two ideas are in conflict.
The good news is that it sounds like you've set up a new organization; so at least some of the baggage that goes along with trying to shift the culture will be minimized.
I would first start by downloading a copy of the CMMI for Development from http://www2.blogger.com/www.sei.cmu.edu/cmmi and become familiar with the various process areas associated with Maturity Levels Two and Three. I would also recommend that you complete a CMMI training course conducted by an SEI partner in your area. The biggest problem we face as appraisers is working with an organization that misinterprets the CMMI model because of lack of training and/experience. The course alone won't solve all of that, but it will sure help get you started.
The next step is to take a look at the processes you already have (you have them, even if they're not written down) and conduct an inventory and compare that to the model. Some will be there, some will be missing, and some will just not be "aligned" with the model (e.g.; you may practice an "alternative" that looks and feels different than the practice in the model).
Remember, in the CMMI the Specific and Generic Goals ("SGs" and "GGs") are REQUIRED, and the Specific and Generic Practices ("SPs" and "GPs") are EXPECTED. Everything else is just information and suggestions.
Next, I would recommend you spend some time learning about how Agile and CMMI can work together. One place to start is to download "Agile CMMI" from our website at http://www.broadswordsolutions.com. It's located on our "Resources" page and will give you some insight into interpretation and philosophical issues related to both. There are several other excellent articles on the web available for download. One I recommend you search for is by Steven Baker and is titled "An Agile Organization's Journey to CMMI Level Three."
Getting to Level Three "ASAP" may prove problematic for you. It can be quite a bit of work (depending on your current state) just to reach Level Two and I would recommend you strongly consider taking a measured and deliberate approach that starts with achieving Level 2 and then gradually moving to Level 3. The Agile CMMI download has some sample work plans you can look at for ideas. That said, it's entirely possible you are further along than you think.
Once you believe you are "close" to filling in any process gaps, you might consider having a lead appraiser come in to conduct an "informal" appraisal - just as a check and to identify any gaps that may need to be filled.
He or she will be able to determine how soon a formal SCAMPI Appraisal can be performed.
Best of luck to you!