How much can I improve my score?

I’m a junior in high school, and I took the ACT for the first time a few weeks ago and got a 26. (28 in english, 23 in mathematics, 31 in reading, 21 in science) I had no preparation whatsoever beforehand and did not study (I wanted to take it the first time as a benchmark to see how well I would do without prep classes or a tutor so that I would know whether I would need one or not).

I know a 26 isn’t too great, and I plan on taking the ACT again sometime in the following months and I will be taking a few prep classes and will also use an ACT guide to study as much as I can before I retake the test.

So I have two questions:
The next test is in February, and after that, April. Ideally I want the next time to be the last time I ever have to take the test and I want to do extremely well; should I wait to take it until April so I can utilize as much time as I can to study or take it in February and get it over with?

And my second question is how much could I improve my score if I took prep classes and used my prep guide alongside that? I want to get at least a 28.

(I’m sorry if these seem like stupid questions in advance, the whole ACT thing is just sort of stressful for me)

I think the general rule of thumb is retaking the test once gets you the biggest jump in score; subsequent takings tend to have diminishing returns, although YYMV. So many things can go into a good test or bad test day: how you are feeling physically/mentally, the specific test, environment, etc. I think you have a great chance to hit that 28 and beyond with test prep. As someone mentioned on another post, practice taking all the sections of the test in the real allotted time as test fatigue can be a factor and you will need to be prepared for that.

I don’t know what schools you are looking at to tell you if 28 is enough or you will have to try for higher. D took a prep class in the fall of junior year and scored a 27 on a practice ACT. Some self study with books and online stuff got her through to the test in May - she scored a 31. She could have taken it again in the fall of senior year and maybe bumped up a composite point, but she didn’t feel she had the bandwidth to do any more prep than she had done already to make it worth taking again, so we didn’t push her.