I'm a big fan of the cast metal blocks and deadeyes from Bluejacket (www.bluejacketinc.com). There's no way I can tell how many you'll need, or in what sizes. It depends on how thorough a job of rigging you do; there are lots of perfectly legitimate approaches to that question.
If you install all the standing rigging and the basic running rigging, you'll probably spend somewhere in the neighborhood of $100 on blocks and deadeyes - wherever you buy them. But, as you've noted, there's no reason in the world to buy all of them at once. My suggestion is to buy a dozen of each of the three smallest sizes of blocks and the three smallest sizes of deadeyes, take a good look at them, and compare them to your rigging plans. Then you'll be able to make an intelligent decision about what you need - and when in the construction process you need it.
If you're serious about doing a good job of rigging the model to scale, the first thing you need is a decent set of plans. The rigging diagrams that originally came with the Revell kit weren't bad, but the ones in the current Revell Germany issue are an incompetently-drawn travesty. The whole instruction book is a scandal. The moron responsible for the finished model on the front page couldn't even figure out where the vac-formed "sails" were supposed to go.
To my knowledge the best available plans of the Alabama (indeed, the only reliable ones available) are those in Andrew Bowcock's "C.S.S. Alabama: Anatomy of a Confederate Raider," published a few years ago by the Naval Institute Press. Here's a link: https://www.mca-usniforum.org/webstore/shopexd.asp?id=18770 It's an expensive book, but an excellent one. (You probably can find a better price at some other web book dealer.) Mr. Bowcock did a remarkable job of ferreting out information about that famous, but historically rather elusive, ship - including a couple of photographs that I hadn't seen before. Be warned, though: the book will make it clear just how inaccurate the Revell kit is.
Hope that helps a little. Good luck.
Youth, talent, hard work, and enthusiasm are no match for old age and treachery.