I'd say to get a better tuner than the Boss - like maybe a Polytune or Turbo Tuner.
As for a comp - the BBE Opto Stomp gets my vote.
Chorus - the Boss CE-20 twin pedal would be great. Big, yes, but programmable and flexible.
I'm partial to rotary speaker effects too, so I'd want my RT-20 in there, though if you are working in well equipped studios, they may have a real Leslie.