How to start on first small PCB design
There are multiple stepping-stones here:
First you need to commit to a microcontroller brand. You will need a programmer and software. (the software is mostly free, programmers are not). Your uni probably has programmers, so depending on their equipment this selection may have been made for you. (unless you want to purchase your own programmer)
Once you have selected a brand I would look for evaluation boards. For example the AVR Xplained boards are excellent, but all the brands have the equivalent type of boards. Your uni probably has a bunch of those as well, if not most brands will send some to your uni for free. (Under the motto: Get the students hooked, and they are likely to select our brand when they go into their professional career.)
As well as beeing great for getting to learn the required programming tools (that I belive will be the trickiest part of this project), these evaluation board are also a solid reference for your own board. The layout, components and  general infrastructure can be copied from these boards.
Then on to the design itself: Here you have (in my opinion) two options: Your uni probably has some sort of student edition of a mayor CAD brand where it's ether free or at a huge discount. Or: you can use Kicad. That is open source, free and quite good. There are many other CAD softwares as well, but I don't really see any reason to delve into these niche lowcost/free softwares. Kicad has a massive and active userbase and tons of user-made content and tutorials. In my opinon that fact alone makes kicad the ideal CAD to get into when designing your first PCB.
Designing the board is partly learning the CAD and partly learning the electronics. As you have a functional circuit with the ESP, and more than likely will have a evaluation board with a functioning microcontroller your task is to &quot;melt&quot; these two concepts on to the same board. Absolutely possible, even with very little experience.