It would really depend on what kinds of effects you have I would think. If by "artifacts" you mean things like string thumps and whatnot, putting the HPF first in the chain should still get rid of that. Filter and synth pedals could still generate some low frequencies, but depending on your setup you may want to keep those in.
And for instance if you put your compressor before the HPF, you are wasting compression on something you're taking out anyway, right? Makes more sense to take it out further upstream, and then you can really dial in the compressor to act how you want it to.