If you have an Apple or it's in the budget..... GarageBand (free with Mac's OS) will take you a long way, surprisingly. Something to keep in mind, is you'll need a sound-card / interface. M-audio has some budget gear... Lexicon too. You'll have to spend at least $500 for something nice though.
Most of the interfaces come with recording software. Assuming you're gonna need an interface, you might want to start with the software they'll come with. After that, you might want to look at the Cakewalks', Cubase, Ableton Live, Fruityloops and all. Protools isn't the best option for Midi but does accommodate it.
If you're goal is to get it to PC, and digital.... don't waste your money on outboard programmers, synths, drum machines or other hardware..... you're gonna need a decent interface to begin with. With a decent software, you can do all of that after the fact.
Consider a decent "USB" midi keyboard controller (very affordable usually). There are countless options for midi controlled synth and sequencers that plug in and work together with the recording software. Not necessary, but a keyboard will make things easy, and keep a musical element to getting into the digital.
Let us know how it goes.....Good luck and keep at it!
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