An equatorial mount and a computer controlled mount are two different things. A mount can also be both.
A equatorial mount has one axis aligned with the spin of the earth (pointed towards Polaris for those north of the equator.)
A computer controlled mount is a mount that knows where the objects in the sky are. You can say, "point at Jupiter" and it will point there and then track the object.
The more you get into astrophotography the more you will spend. It is quite fun, addictive, and rewarding. The mount is critical for your success for deep-sky objects. (Nebula etc...)
You have a lot to learn but get started on wide field astrophotograhpy as Matt recommends, it is much cheaper and you'll get a feel for it. Then start hanging out in the astrophotography forums at CloudyNights.com.
Modify your DSLR for astrophotography is necessary for certain deep sky objects, but don't do it just when you start out, you'll have so much learning to do it will be money wasted. After a year you'll know if you want to shoot deep sky or not. But when you do, you can get images like this:
That was taken with a modified Canon 40D, 9 exposures, 2 minutes long. ISO 800, through a 5" f8 archromatic refractor, mounted on Celestron ASGT computer controlled equatorial mount. I had to discard about half the frames because the mount wasn't perfectly polar aligned and/or I had gear train periodic errors.
And this is only the beginning...