As one of the preparation practices before starting the actual Lamrim meditation, I try to develop Bodhichitta. My understanding of bodhichitta it is the wish to attain Buddhahood to benefit all sentient beings and it's both compassion and wisdom. During this phase in my meditation, I try to generate a feeling of compassion and I'll contemplate those who I know are currently suffering (such as the people in Japan), or even friends I know who're undergoing a tough time, and I'll try to single pointedly focus on this feeling. I'll finish this phase of the prepatory practise by repeating the prayer, 'Through the virtues I gain by giving and other perfections, may I become a Buddha for the benefit of all" several times.
But I'm not sure if I'm doing it right. Am I on the right track?
Every approach that opens the heart for suffering beings is "on the right track". A further step is (perhaps later) to also consider specific persons one cherishes, has neutral feelings to or even hates ... to generate an even attitude of love and compassion toward all beings. The generation of bodhicitta works most efficient when including persons one knows in one's meditation and this way it may have a direct effect on one's daily conduct.
I sometimes feel that I rush the prepatory practises so that I can get stuck into the main body of the Lamrim meditation, as I feel more keener to meditate on 'Our precious human life' (for example), rather than go through what can feel like the mundane prepatory practises.
Also, once I'm on the main body of the meditation (such as 'our precious human life'), it often feels like I'm doing more reading than meditation. At the end of each meditation, I try to recall a pertinent point, such as 'don't waste my precious human life on less worthy distractions, when I could be practising dharma' and I'll meditate on that, but as I say, it mostly feels like reading than meditating. Will this change as I become more familiar with the text?
The more you study Lamrim the more the thoughts will become natural. Take a rest every now and then and contemplate what you have read. Watch the qualities of mind that arise depending on this Lamrim mind training. Recognize how conducive it is.
Also all the different aspects enhance each other. E.g. contemplating the suffering of the lower realms may cause right effort as to oneself but may also help to generate compassion as to others that have not been taught these precious teachings and thus are blind toward the effects of their deluded actions and will have to endure so much suffering that is even worse than their current suffering. The same holds true for the type of sufferings contemplated in the context of the persons with medium capacity.
I find it very helpful to also generate an appropriate grateful attitude toward all the teachers that teach the lamrim and toward this great compassionate teacher, Lama Tsongkhapa, who has written this great teachings as gift for future generations of beings. As you read the text you may keep him in your mind, even visualize him smiling and caring, teaching you to foster the best of benefits that may arise for you based on his teachings, like a father teaching his child.