Jak,
I am currently in a prog-metal project.
But the thing is use of effects (the quantity and types) is much more a personal thing than genre based.
Right now I am running:
EHX big POG, for organ type sounds (I love classical organ music)
Big John Hairy Balls, agressive fuzz(/distortion)
Line 6 RotoMachine, rotary speaker effect: my alternative for chorus, it's more transparant than chorus IMO
Goatkeeper v2, it's just an evil tremelo especially when combined with fuzz
volume pedal for violin-like swells
delay, right now an analog but going to go back to digital again for clean short delay without side-effects
In my rack I have a TL Audio Mono Valve Processor, it's a tube compressor + tube semi-para 4b equalizer + noise gate.
I love that in a rack unit because it's constantly on for my overall tone.
But my problem in the progressive metal project is that I want to cut down my effects arsenal.
Organ emulation: I play with a keyboardplayer.... so he can provide much better organ sounds. Making my POG absolete.
Fuzz, although the Hairy Balls sounds wonderful on bass and our guitarist is envious about the sound and encourages me to use it, I rather keep playing clean when the guitarist is playing with heavy distortion. I feel when playing alongside him I don't need any fuzz/distortion on my sound.
Goatkeeper v2 is something weird and fun... but it's not musical enough for the things we play.
When jamming with the band, more talented musicians than I am, all I want to do is keeping an incredible cutting through lowend without any thrills.
Rotary speaker effect and delay are very usefull on mellower parts.
So basicly, it's all very personal, you need to figure out yourself what you want.
So from my experience I would suggest you try out chorus (or rotary speaker) and delay. Maybe that can be usefull effects for you.

my 2 cents