Congrats on the choice to grow. What side of your house are you considering? I'd recommend the south side - the more sun they get the better.
For your first year, you should be able to get two plants to grow up a 4' wide x 8' tall trellis (one on the left side and one on the right side) and keep them apart relatively well. If you grow plant A on the front of the trellis and plant B on the back side, they're going to intertwine pretty quickly - making harvesting a particular plant nearly impossible. By your 2nd year and for sure by year 3, they will grow together and harvesting could be challenging to differentiate which hops go in which pail. Also, If it's a wood slat trellis, be sure you can get to the back side relatively easily - there will be cones back there at the end of the growing season.
Regarding the tree, It depends on where you are and the size of the tree. Keep in mind that the wind is going to blow the tree around, and if you get any good size storm, it could pull the eye bolt out of either the tree or the top of the trellis - and this could damage whatever is growing on the rope at the time.