Yeah, I work a lot with numbers and computers and such and I have the same enjoyment of making something tangible.
A good place to start is to get a few decent chisels, a little handsaw (western or japanese, as long as it's sharp), and practice making some joinery by hand. A few books from the library will get you started in the basic technique (there are many good authors out there). Use something cheap like scrap poplar just for practice. Even if you end up using only machine tools later, the things you learn by doing this will be good skills down the road. It teaches you about accurate layout and gives you a feel for how to work the wood compatibly with the grain.
After you've done a half dozen or so mortise and tenon joints and dozen dovetails, you'll be itching for something more. Maybe try a small bookcase, small hanging cabinet, or possibly a side table. You might be tempted to make it out of a really cheap wood (like poplar again) -- but don't. If you can afford it, then make it out of a wood that you like, even if it costs a little more. At the end of the project you will care more about the labor you put into it than the modest difference in wood cost.
If you want to get into using the table saw straightaway, the best projects to make on the tablesaw first are jigs. Tenoning jigs and crosscut sleds are extremely useful. Just be sure to understand all the saw safety rules, understand what causes kickback, don't remove the safety guards and pawls, and don't get in a hurry.
Good luck, Nate