First off, welcome to the forum! This is a great place to ask questions, learn, and share from your own successes and failures - and we all have some of both to share!
With regard to progression, I don't think there is any single path that is best for all. I agree with Al that it is good to make some quick-maturing cheeses at first, to get quick feedback on how you are doing - but there is a wide variety of cheeses that fit this bill, depending on how you define "quick." Two key questions are going to be what kind(s) of cheeses you like - no reason to make a cheese you don't care for just because it is "supposed" to be next - and what equipment you have, especially your ability to press a cheese.
Starting with a no- or low-press fresh cheese, with no aging other than perhaps a couple of days in the fridge, will give you a quick introduction to cheesemaking and can give very quick feedback. Pressing can be done simply with a jug of water or a canned good.
From there, if you don't have a press, you could go the direction of mold-ripened cheeses, which require no pressing - camembert/brie/etc., or blue cheeses such as a stilton. These are not generally considered "beginner" cheeses, but they are really not that hard. A camembert can be ready in 4-6 weeks, depending on your aging facilities; a blue will take more like 12-14 weeks, so not as quick on the feedback.
If you do have a press, you could go the route of Caerphilly or Lancashire, which ripen in 3 - 6 weeks. These are both considered to be in the cheddar family, but don't require the 6 months or more of a true cheddar.
Many folks here on the forum advocate working with one cheese make over and over again until you really get it perfected. This is good advice ... which I did not take. There are some cheeses that I have made many, many times, tweaking my process each time until I consistently get the results I want, but rarely do I make the same type of cheese twice in a row. The 90 or so cheeses I have made include more than a dozen different types - I just like to experiment.
The key, as you allude to, is keeping records so that, the next time you make a particular variety, you can compare, adjust, etc. Currently I just use a spreadsheet, with columns for the date, ingredients, type of make and source of recipe, description of the make (the steps), and notes on what happened. I include test points for temperature and pH only where they seem to matter. Others on this forum use much more detailed make sheets, keeping closer track of time/temp/pH along the way.
From time to time, different users here have talked about developing some software to keep a cheese log, but I have not yet seen anything suggesting anyone has followed through or finished any such program. That includes me - I started work last summer on a program to keep my cheese log, but it is not yet finished, and won't be until at least this summer - the first time I will possibly have time to do more work on it. Certainly if/when I complete it, I will make it available here, complete with source code, for the edification and/or critique of fellow members. But meanwhile, I keep using my old spreadsheet ...