In addition to all of the excellent advice that is being given here, I would like to add:
Be sure you work on triad arpeggios so you can play a triad from the lowest possible note on the bass to the highest comfortable note. I notice that some students try and play 7th arps up and down the bass and they don't really have the basic major, minor and augmented triads nailed down. You can approach learning triads like this:
C Maj triad (from lowest possible note)
E, G, C, E, G, C, E, back down, C, G, E, C, G, E
then change one note and play an A minor triad arpeggio (A minor is the relative minor of C Major)
E, A, C, E, A, C, E, back down, C, A, E, C, A, E
then go to F Major, the next major key in the cycle of 5ths:
low F, A, C, F, A, C, F, back down, C, A, F, C, A, F
then change one note and play D minor triad:
low F, A, D, F, A, D, F, back down, D, A, F, D, A, F
and keep going around the cycle.
If you want to add an augmented triad as an extra passing chord between the major and minor triad arps, you can also do that:
(between C Major & A minor) E, G#, C, E, G#, C, E, back down, C, G#, E, C, G#, E
Mastering the triads will give you a lot of facility around the bass and it will help you with the 7th arpeggios.
Good luck!