A little bit of time spent with some basic theory might be a good idea - specifically, a half decent knowledge of the basic arpeggios (up to the 7th) will work wonders - you don't need to know why they work (although if you do that would be good too), just learn where to find them.
To get you started:
Maj 7th arpeggio - Root 3rd 5th 7th
Dom7th arpeggio - Root 3rd 5th b7th
Min 7th arpeggio - Root b3rd 5th b7th
There are others you'll need if you want to do it properly, but these will get you started. While you're learning you can just use the chord names off the charts and play whatever arpeggio best fits each chord:
Here's an example (taken from Autumn Leaves as it happens):-
Dm7 G7 Cmaj7 Fmaj7
You play D F A C (Dm7) G B D F (G7) C E G B (Cmaj7) F A C E (Fmaj7)
Start off playing them slowly as shown - as you gain skill you can start exploring more subtle sequences,
e.g. D F A C B G F D C E G B E C F A
There's lots of variations, and not nearly enough space here to go into it properly. Walking bass is actually quite a big topic, but the basics are really straightforward (and lots of fun if you're prepared to put some time into it).
Enjoy.