I did a single swing for the small boy a few years back and I would think about what happens in five years when the children aren’t so bothered with a swing. By this time the chances are that timber will have started to rot at ground level
First thing to consider is whether you want to put the poles directly into the ground or whether you can use a metpost-type arrangement to avoid rot and concrete. An annual poke around at ground level with a screwdriver will help monitor rot, then an inspection of ropes, joints, etc
Less concrete used means less to remove when you want to reinstate the lawn; I used a 6″ post-hole auger and worked by eye off an erected frame to get the angle. You might be confident enough to use a 4″ auger, I wasn’t 🙂 Don’t forget to space the holes according to what will be ground level on the frame. If the length of the base of the triangle is adequate, then 2′ will be adequate in the ground; scale some photos or measure some examples
I can’t help you massively on crossbar dimensions, it’ll vary according to child size and swingage