I suggest starting someplace near entry level, depending on where your current level of understanding is. What I see a lot on this website are many examples of individuals who jump in without any basic understanding and then find themselves lost.
An understanding of current, power, and voltage drops should not take long for an ME to pick up, probably an hour or two. The an understanding of components and their effects and limitations would come next. A study from an AC circuit analysis textbook would be appropriate.
The school that I graduated from did teach the ME students that much, just as the EEs had to learn statics, dynamics, and strength of materials. We were not masters of the subjects, but certainly literate.
At that point building projects and using micro's and paying attention to how the I/O portion actually works would be reasonable.
Still remaining would be gaining an understanding of op-amp and comparator functioning, which are quite important since not everything is best done by software.

Not so sure about the AC circuit reference. DC would be better in my opinion. You can buy a decent continuously variable DC power supply unit (up to 32 VDC) for relatively little money (about £30) that will enable you to built any breadboard project that takes your fancy. The AC equivalent is a bit pricey for an entry level student. If you can find one.

 

Not so sure about the AC circuit reference. DC would be better in my opinion. You can buy a decent continuously variable DC power supply unit (up to 32 VDC) for relatively little money (about £30) that will enable you to built any breadboard project that takes your fancy. The AC equivalent is a bit pricey for an entry level student. If you can find one.

DC circuit analysis is the first and most basic part. Evidently I was not clear in saying that part.