First you need to accept that anything you may do to your brand new console may kill it. You'll probably want at least two consoles to compare between the two. (Swap flash memories and see what happens.)
Next, pick a piece of the system and dig into it. You need to develop a very finely detailed understanding of your piece and how it interacts with the rest of the system. Take lots of notes. There isn't anything more frustrating than finding something, but not being able to recreate it. Post your findings. Document what you know to be true and what you think is true (or false.) Others who are interested in the same piece will interact with you. I suspect only a small percentage of what is known gets posted to an open forum. In any event, ignore the naysayers (that'll never work, the hypervisor will prevent it,) they are trolling for MS.
//forum soapbox on
The sense of accomplishment you get from breaking a system is incredible, but before you release a mod into the wild I would encourage you to consider the consequences of your actions. C4EVA did some amazing work on the DVD drive, but also seriously damaged the homebrew effort. The pirates got what they wanted, and quit working on cracking and started downloading instead.
//forum soapbox off
For another form of mental challenge, play around with a console that has already been hacked. I've wanted to retrace Bunnie's work on the XBox for some time now, but haven't gotten around to it yet. Kind of like building a replica of the Wright brother's flyer and taking it out to Kitty Hawk.
All for now,
VAX