First of all I applaud your transition as I myself am currently undergoing this as well

As far as nutrients go, daily mutivitamins are definitely recommended for vegans. Just make sure they are free of animal derived ingredients.
Now that dairy is out of the question, replacing milk with soy or almond milk will give you all the nutritious elements of milk without all of the cholesterol and negative side effects.
Purchasing soy cheese, yogurt, mayo, etc all contain soy ingredients which will seamlessly transition your diet from intaking dairy's nutritious elements to soy's similar nourishment.
Hope this helps
