Actually, you probably don't strictly need a microprocessor - after all, early MIDI managed with just a UART and some discrete logic!
In fact, with VHDL, FPGAs, etc, it may actually be more true today!
But don't let me put you off; an 8051 is a perfectly reasonable solution - just bear in mind that software is not the only solution!


Again, you do not actually need an IDE.
It is perfectly feasible to use just a text editor of you choice, and invoke the compiler etc from the command line.
You may find an IDE more convenient in giving you point-and-click configuration, online help, shielding you from the arcane world of command-line switches, etc, etc, - but it is by no means essential.
On the other hand, an IDE editor is often weak when compared to an editor from a dedicated vendor (eg, CodeWright); IDE project management is often weak when compared to the flexibility of custom makefiles; etc, etc, etc, ...

As a beginner, I would probably recommend that you start with an IDE such as Keil's uVision - if you find it adequate for your needs, that's fine; if you find it's cramping your style, there is nothing to prevent you moving on to the more flexible & capable dedicated tools.

You can download a free Evaluation version of Keil's tools from their website - but be sure to read the limitations of that free download!

If you do download Keil, please be sure to read the uVision Getting Started guide, and work through the example projects in it before starting on your MIDI project - this will save you the embarrasment of a whole load of "RTFM" comments! ;-)

PS
Please don't take any of this as criticism - you show an admirable attitude of commitment to actually doing your own work on this project, rather than just demanding code.
Well done!