For your posts, I like JUMBO 4x4 posts(4 1/8" x 4 1/8") verses std 4x4 posts (3 1/2" x 3 1/2") and 8 foot tall.

The last fence , I built, Home Depot had them in stock. Just take your tape measure to be sure.

For setting post, just use gravel or pebbles/stone (not concrete or quickcrete) Unless you are in a really high wind area, or maybe your "gate" post(= extra weight hanging on the post). My neighbor(ex-carpenter,now chemical engineer) put me on to using stone verses concrete. Worked good. The old posts always rotten away just above the old concrete at about 2-4" below the soil level. Moisture just sits there, but with gravel or stone, that moisture can escape and increase the longevity of your post, overtime. You can still leave the gravel/stone at 2"-4" low and add soil/grass above to the level of the lawn, for appearances. [And yes, your post will be tight with gravel or pebbles, plus replacement, if needed, is easier than concrete, too]

Just pull a string line(at roughly ground level), very tight, for your straight line.("lift and drop" line in the center, so it "finds" its own straightness).

Mark holes(dig out a circle of sod with a "tile spade"), loosen string, and dig your holes, then reattach lower string, tight, and now add a top string, tight, also (for post height and level). I do also use one of those $8 post levels, too. They attached to the post with elastic=very handy. They have two bubble levels built-in.

Put your post in, at a distance, at just slightly under 8 feet apart(from side of post to side of next post), thus you can always trim/cut/saw a 8 foot board to go between the posts for your horizontal supports. [I'd rather be 7'11" than 8' 1", and have to go buy a 10 foot board to fit that one stop]