The first thing I would suggest is a thorough reading through the "getting started" section of the DH wiki, and then working through the subjects you have just mentioned. After doing that, when/if you have specific questions, someone here is very likely to be able to provide some help.
I just must make a comment here about that section of your post.
It might not be really "fair" to refer to that "previous hosting guy's" arrangement as "making a killing" as a result of another's inexperience. For many "business people", who are not "saavy" with internet related stuff, such an arrangement is rather common, and really shouldn't be evaluated in terms of bandwidth/storage metrics.
$500.00 a year breaks down to $41.66 a month, or $9.58 a week, which is a completely insignificant expense for a business in exchange for "problem free" hosting of a website (and managing of email, backups, admin duties, etc.). Even if a business has someone in their employ who can handle all these things for them, it is very easy for the cost of that person's time to handle such things to greatly exceed such a fee (unless that person is making a buck an hour!).
Such an employee's time spent on "managing the webhosting" also is time not spent on other business related tasks, which increases the cost to a business even more.
Sure, on the face of it, that arrangement was "a lot more expensive" than what one can get with a Dreamhost account - but that does not necessarily mean such an arrangement is a "bad deal" for a business. For those of us who are interested in such technologies, and have the time and resources to "diddle around" with such things ourselves, Dreamhost is a great deal; for a business that doesn't want such things to become a regular function of an employee, the other arrangement may actually be a much better business decision.
At any rate, welcome to Dreamhost and good luck with your migration. The wiki, and the internet in general, is a great resource for planning such a move with lot's of information available. Don't forget to allow time for DNS updates to take place, and I suggest you completely "stage" your site(s) before initiating DNS changes (the wiki has lot's of info on that, and so do many previous threads in these Forums).