That's some nice tidy prog there! I love the long instrumentals, lots of delay and stuff happening especially with two guitars, so you don't really need to be that adventurous with your effects really. I suppose that is a joy of being in a three-piece!
Like many have said, a good overdrive is pretty pararmount. It really is a standard effect for bassists now, so that would be where I would invest most of my money if I were you. However, I have a 20 pedal mammoth board so I'm probably not the best person to talk to about keeping it simple.
Even so, three most essential pedals, in my opinion: TUNER (above all else), Compressor and a decent DI. I really couldn't gig without my TU-2, MultiComp and my MXR M-80.
A SansAmp DI or an M-80 would both also produce a decent overdrive, although both sound entirely different, so listen to them both first. I went for the M-80 as it has independently switchable distortion, seperate from the EQ, unlike the SansAmp.
+1 to a Fuzz, that would sound really cool in your band situation, from listening to your songs. I think there's probably enough delays going on, but a nice overdrive or fuzz would sound great.
Since I got my Octaver though I haven't stopped using it, so maybe that could be something to look into? Great for filling out sparse guitar parts and bringing home the funk!