I recently ordered some 3/4" engineered hardwood and am looking to install it floating over a concrete slab (also using a plastic moisture barrier and cork underlayment).

The layout of my townhouse is illustrated below (it's 2 floors). The area boxed in red will be porcelain tile and the bathroom is also tile. Everything else will be the engineered hardwood. The question I have is, where is the best place to start installing?

My initial thought was to start in the living room on one of the side walls, but after some more thought, I was thinking that it might be better to start in the hallway (where I have the blue arrow) since that is the place where the longest and straightest boards can go. Similarly for the upstairs, should I start in the hallway as well?

Thanks!

Image Link:
https://ibb.co/FXxr27q

The hall would be my favorite place to start. Once the first wall in the hall has been started, a helper could also work to fill in the next room at the main room end of the hall, working away from the starter rows.
I like to clamp several rows together so the glue can set, then slide everything back against the starter wall where the shims can hold everything in alignment.

Thanks Pete! Once I start in the hall with the starter row, once that starter row extends into the living room, how do I work off of a row that's in the middle of the room? Should I glue the first row down to the underlayment? How do I prevent that starter row from wobbling back and forth as I work off of it in the living room since it's in the middle of the room and not the edge?

Working on the first rows is always dicey until the glue that holds the rows together has set up. This is where a few clamps that hold all the rows tightly together really pay off. 18 or 24 inch bar clamps can press the rows together until the glue sets. Once the glue sets up, you can slide everything back to the starter wall.

I think that the hall is the best place to start but you must do what is convenient for you and which won't bother you. From the floor finishing point of view, you can consult the professionals like Home Quality Remodeling for the best advice on this.

24 inch quick release bar clamps are what I use for the first three rows. Then you can use spacers at the walls to give you the expansion gap after you push the rows against the wall, again.
If you have clic-loc joints on your floor you will not need the clamps.