Learning the polite form first will allow you to construct basic sentences quickly that don't sound rude - and the -masu form is a little easier to learn than the plain form initially.
I am teaching myself, I learned the -masu form first, and it allowed me to pick-up on patterns that have proven useful as I have progressed to more advanced topics. For instance, the polite positive past form is -mashita (tabemashita, ikimashita, etc.). And the plain positive past is the -ta form (tabeta, itta, etc.). Interesting how they both end in -ta... (check out the past forms of adjectives...)
I suppose you could pick-up on this pattern at any time - but I do think learning the -masu form first is a good idea - and hey, it takes like 4 minutes. Then move on to the plain form - I would and did learn it in this order: -masu form, -te form (and -ta form), plain form, then all others (potential, conditional, imperative, etc.).
But Mike is definitely right (he always is BTW), you'll eventually need all forms, and instructor's lessons (and most texts) are very well planned and tested - so just enjoy the ride!