Well, I would beg to differ on Bossel's opinion. Mandarin, unlike Japanese, is extremely dependent on the tones, where a slip in tones can render something said to be non-comprehendable or starkly different in meaning.
So, I reiterate, get down the tones adequately and remember them before proceeding with the course. Dreamer, as you have a teacher from Beijing, i.e. a native speaker, this should not be a problem.
Regarding accents, don't worry too much yet unless you want to ensure that you only desire a certain accent. Most teachers from either China or Taiwan will be teaching in the Standard Mandarin accent - 标y•'Ê话 - which is the formal accent spoken in both places, similar to the standard North American accent (in the US) or the Received Pronunciation accent (in the UK) for the English language.
You mention that you know 'bits of Taiwanese Mandarin'. Make sure this isn't just a very broad generalization, in the sense that you tend to pronounce words without much 'sh-', 'zh-' etc. sounds - many Southern parts of China speak like that, including Shanghai.
Taiwanese Mandarin has specific peculiarities for words as well as the accent - a simple example for the former would be the word 'bicycle': Ž©s车 - zixingche (China) and 腳"¥ŽÔ - jiaotache (Taiwan). In casual and non-formal situations for instance, Taiwan Mandarin always prefers the pronunication of 'si' as opposed to the Standard Mandarin pronunication of 'shi', for ¥. As you have a teacher from Beijing, you're not likely to be able to learn Taiwanese Mandarin, if you so desire. Nonetheless, it can be developed at a later stage, if you go to Taiwan for instance.
I personally speak in the Standard Mandarin accent myself for Mandarin. However, people from Hong Kong generally tend to imitate the colloquial Taiwanese accent (which is closer to Cantonese in similarity), but not very well in the sense that it sounds too much like Cantonese. This also goes to show why tones are important at the outset; and try hard to ignore your Cantonese pronunciation tendencies when remembering them.