gogoflying well done for thinking safety first but some points;
1. The ICAO schematic indicates crossing the upwind end of the runway at 90 degrees and then turning 90 degrees onto the downwind leg but this is not quite the case in flight.
2. In still air you should allow for the radius of the turn to complete the turn at the downwind point and not halfway along the leg. This will require a crosswind leg which is offset upwind.
3. A wind will blow you into the downwind leg prematurely therefore lay off further into the wind to prevent this.
4. Offsetting in the above way provides for a better sight of aircraft already established further upwind and tracking to the downwind point (such as aircraft performing circuits).
note; turning onto downwind midway along the downwind leg will blank out vision of any aircraft already positioning at the downwind point, especially when flying a low wing aircraft.