The lav wet vents the shower and the toilet.
A 3x3 wye for the shower, then a combo or wye fitting to pull off the shower, at the wall a long turn 90, going up to a 3x1.5" santee.
You can have an end of the line cleanout here.
The trap arm is 1.5", and you can use a 1.5" trap with a 1.5x1.25 slip joint washer for the tailpiece.
The first drawing on the page doesn't pass inspections.
The santee on it's back for the toilet is a bad idea. Waste plopping down spreads both ways.
If you need an end of line cleanout, then that would be run in 3" to the wall for the lav. A 3" cleanout with a 2" reducer on top for the lav and vent.
This drawing is showing horizontal wet venting. Since the vent for the shower and the toilet is being washed with the lav, you have the ability to snake the line if needed to keep things clear. You don't have that option with a dry vent below the flood level of the fixtures that way it was drawn before.
Fittings below flood level should be what we consider waste fittings. No "vent" fittings allowed.
On the horizontal you are looking at wyes and combos. No santees.