Arduino, suitable platform for MIDI sequencer?

I’ve recently completed a Monome 40h kit which has been awesome and it reminded me how interested I am in electronics and the Arduino platform in particular.

I’m an electronic musician and prefer working with hardware over software. It would be fascinating to develop my own platform for a MIDI hardware sequencer.

Before I embark on a potentially steep learning curve, in the briefest terms, is my ultimate goal for this platform a realistic one?

Off the top of my head I guess my expectations are as follows.

MIDI in/out
Step record (MIDI data input not in real-time)
Normal record (MIDI data input in real-time)
An LCD display and possibly various LEDs for UI output
Buttons/possibly numeric keypad for data input
Some kind of permanent data storage

For the last one I saw a MicroSD “shield”. I understand the shield concept but can a single Arduino board support more than one shield? So might the above involve an Arduino and then various shields to support the I/O?

I’d like the hardware aspect to come quite easily, off the shelf solutions in other words as the bit I’d really like to get stuck into is the programming.

Thanks for any input.