Everything is dependent on style and personal taste as far as how you want to use effects. It also makes a difference if people will mostly hear you through a PA versus a small venue where they will hear a lot of the direct sax sound. If 50% of what they hear will be your direct unprocessed sound, then you can mix the effects wetter (dry is none or very little of the effect in the mix. Wet is more of the effect). One other thing, if you're doing multiple effects fine tune each effect to optimize the settings. Then turn that one off and work on the next one. When you engage 2-3 things you might need to tweak certain things because they interact.
Listen to how other players use effects, it doesn't have to be horn players. Some horn players known for interesting effects would be Eddie Harris, Randy Brecker, Michael Brecker, Bennie Maupin, John Klemmer, Bob Mintzer, Tower of Power, Klaus Doldinger, Joshua Redman, Brian Donohoe...but you can listen to players on any instrument like Jan Hammer, George Duke, Herbie Hancock, Allan Holdsworth, John Abercombie, Hiram Bullock, Mike Stern, Jean-Luc Ponty, and non-jazz players too like Jimi Hendrix, Alex Lifeson, Andy Summers, Edge, Pink Floyd, Led Zeppelin, and all kinds of ambient stuff. Whatever you like where the music has been sonically shaped through the use of effects.
Some general things...the order of different effects in the chain makes a huge difference. A lot of people would put a harmonizer/octave effect first. Or an envelope filter. Then things like chorus, phaser, flanger, etc. Usually things like delay and reverb would be last. If you were running something like a chorus, if you want a more natural saxophone sound then you probably want a slower modulation with less depth. Then you have more flexibility with the amount. If you use compression, I would start with just a tiny bit to smooth things out and work from there. I would put that after an envelope filter or even at the very end if it's just a bit of light compression.
There's a lot of stuff written online about how effects work and interact, especially in keyboard/guitar forums. Don't be afraid to break the "rules". I've done some fun synthesizer effects putting delay before a filter that opens an closes almost like a volume pedal. Usually people would say to do the filter first. With the echo, you can get almost a harmonizer effect. Then I put a longer reverb after the filter. You could do something like that with the sax using a pedal wah.
I love all kinds of crazy effects, but since I play synth using a wind controller I use more of the far out stuff there. On sax, I like a bit of chorus and maybe some delay/echo and a bit of reverb. An envelope filter or octave divider/harmonizer if you want to get funky. Using electronics is kind of like recording to me, always try to get the best acoustic sax sound you can. That's the starting point and the better the original sound is the better it will sound at the end.
Last thing, if you have a laptop or iPad there's a lot you can do with virtual effects. If you have a decent audio interface, you can get a free plugin host like Cantabile Lite and setup all kinds of effects chains using free plugins. I like having a graphical interface for each effect separately, versus the menu diving involved in a lot of the multi-effect pedals. That's probably why a lot of people like the individual pedals, although a collection of individual effect pedals can get quite expensive. You could easily work out cool combinations on a laptop or iPad (ToneStack is a great multi-effect app) and then just duplicate that patch on your Line 6 pedal.
Here's a couple demos I did with ToneStack on my iPad