Trying to run to the back without the help of stealth or honor is often suicide. Reptalons can kill with a hit and a breath, and there is a long run where you'll likely see 2-3 reptalons at a time. There are also the spawn traps which will drop either 3-4 air elementals or 3-4 drakes on you at once. In the champ area, it's always drakes.
So to sum up, if you think you can run past Miasma, Rend, Pyre and a gaggle of Reptalons, feel free to try running. Otherwise, use your honor or stealth.
In theory, it would be possible to just invis yourself every time anything targets you, but I haven't tried it that way, so I don't know how feasable it is.
As for what you want to bring? It doesn't matter. Once you get to the champ, anything you bring will work well until the end. Then you will find the tormented minotaur and from what I've heard, anything you bring will get killed.
If you bring a warrior, bring a bovine slayer talisman or a repond slayer. If you bring a mage, a bovine slayer would be best. Just make sure your suit has very good physical resist for the minotaur and fire resist for the drakes.
I haven't tried the champ yet, but I do go back there to pick up artifacts, and usually stay to regain the honor I lost by embracing it to get there.