PCB design software for beginners

Thank you!

Going back to Eagle, I seem unable to get the above schematic done over a 10x10 board unless I enable the bottom layer.
With 1.27mm routing grid it reachs 95%, with 2mm about 40%.
I was trying to keep it single layer, as the fabrication process scared me a bit, but I guess I have no choice.

Another issue I found is it makes some tracks with 90 degrees turns.
I know I must avoid that but I don't know where I can set it.