First of all, it's been said many times before in this Forum but it needs to be borne in mind by everybody: what matters is what satisfies you, and what you enjoy doing. The day a modeler gets intimidated by somebody else's standards or opinions is the day the hobby ceases to do what it's supposed to do.
I honestly don't know what kind of thread Revell packs in its boxes nowadays, but my suspicion is that it's not very good. Experienced ship modelers spend lots of time arguing about the best material for rigging. My own first choice is silk, but my supply of it has dried up. I like the "cotton-poly mix" that's sold by Model Shipways (via Model Expo - www.modelexpooonline.com ); it has a nice, rope-like appearance, good color, and seems to tie well. Some veterans insist that linen is the only "proper" rigging material, but I disagree.
In any case, one of the easiest ways to improve the appearance of a sailing ship model is to introduce a big variety of rigging line sizes. In a real ship the sizes number in the dozens. That's probably more than you want to worry about at this point, but if you use three or four different diameters - with the ones that came in the kit being the largest - you'll be surprised at how much better your model looks. Prototype practice regarding rigging diameters can get kind of complicated - especially in a ship like the Alabama, which (if I remember correctly) used wire for some of her standing rigging. (Wire rigging, generally speaking, is thinner than rope rigging used for the same job.) The general rule, though, is: the higher up, and the lighter the job, the thinner the rope. (It's actually quite a bit more complicated than that, but I suspect that'll do for your present purposes.)
It's almost always a good idea to replace plastic eyebolts and belaying pins. Styrene is wonderful stuff, but it has its limits; by nature it isn't ideal for parts that are subjected to the kind of breaking strain that comes on fittings of that sort. If you've already cemented all your pinrails and fiferails into place, you may decide it's too late to replace the pins. If you want to give it a shot, though, it's not difficult. Slice off the plastic pins, sand (or file) the top and bottom of the pinrail smooth, and drill a series of holes of the appropriate diameter with a pin vise. For the pins themselves you have a couple of options. Aftermarket suppliers, such as Bluejacket (www.bluejacketinc.com) sell some nice turned brass belaying pins - but they aren't cheap, and even the smallest ones on the list (1/4") are pretty big for that particular model. The less expensive option is to use lengths of brass wire, stuck in place with superglue. That arrangement can be made to look pretty good - especially if you round over the tops of the pins, and blacken them (with either a metal toner or paint).
Looping lines around belaying pins is indeed a little tricky, but (like most such tasks in sailing ship modeling) it gets easier pretty fast with practice. One trick: form a loop in the line in such a way that the hauling end passes over the standing end, then slip the loop around the pin underneath the pinrail. Pull the hauling end and the line will be locked in place firmly enough that you can take three or four turns around the top and bottom of the pin in a figure-8. Then put a blob of white glue (e.g., Elmer's) on the top of the pin and arrange the remaining line around it in a loose coil. (Some modelers spend lots of time making rope coils off the model, and glue them to the pins afterward. That works, but I personally have always found it easier simply to coil up the end of the line itself.) I strongly recommend white glue as a rigging adhesive. It doesn't stiffen the line as much as superglue does, and, most importantly, it can always be softened up with a drop of water. You'll appreciate that point the first time you decide to rerig a line, because it either got busted or mysteriously went slack.
Various companies make "rigging tools" to help with such jobs. Some experienced modelers swear by them, but I personally get along fine with four: a small pair of tweezers with sharp points, a much longer pair of tweezers that can reach all the way across the ship, a sharp-pointed metal probe to apply small dots of white glue, and a small, sharp pair of scissors. It's vital that the tweezers be of high quality, with points that match up precisely and clamp effectively at their very tips. Small scissors can be found in various places; again, the key is to find a pair that will cut thread right at the tips of the blades. (Rather surprisingly, perhaps, the scissors on Swiss Army knives work beautifully - though the big red handle makes them a little clumsy.)
Another tool that may come in handy is one you can make yourself in a few minutes. Get hold of a big darning needle and break it at the midpoint of the eye. (If the two sides of the eye don't break evenly, either grind the long one down or get another needle and try again.) Shove the pointy end of the needle into the end of a dowel or stick that's long enough to reach across the ship. The "V" formed by what was the eye of the needle can be used to shove recalcitrant rigging lines under pinrails.
Hope that helps a little. Ship model rigging is full of fairly steep, but short, "learning curves." Stick with it and you'll get better at it - remarkably quickly. Good luck.