Midi keyboard for Roland s-1

Hi everyone! I'm a complete noob and as such, I started noodling with a Roland t-8 and S-1 which I both quite like, except that I just can't play with the keys of the s-1 (size and velocity-wise). Could you recommand a Midi-keyboard that would :

• be cheap (used)
• have an arpeggiator (with multiple patterns would be great as I find it a cool source of inspiration)
• be compact

Also, do you now if I will still be able to use the sequencer of the S-1? Thanks a lot for your help