Weena - We determine the overall number of lifetimes. The order is self-selective, like a jukebox or cd player placed on random, meaning there's no linear sequence. In this case, it's not so random, but based on the next greatest adventure in consciousness, whenever that may be.
The great part for the Renaissance guy is that in his next life, if he accessed the "future" (in his case, his last lifetime) from the Records, he would have the event and response to view (just like we all do for our past now). He would be in a position to tell people in that timeframe, about the future in great detail, as opposed to others (i.e. da Vinci, Nostradamus), who hadn't lived in the future yet, and could only give us events without the full details.
We're always accessing info from the Akasha, but to do it more consciously you want to be in a more meditative state.
What will you experience? You're right - it does depend on you and how you will best understand them. If you use certain senses (i.e. sight, hearing) predominantly in your normal, waking world, those will likely be the senses you initially use in the Records, until you choose to expand to a multi-sensory experience. If you're visual, the experience might be like a 3-D version of the movie "Avatar", or "What Dreams May Come", or the even like the scene in "The Golden Compass" where the little girl looks at the symbols on the compass and then goes "inside" it to see pictures. Then at some point, the experience gets to be similar for everyone.