Hi Harvey, I'm a fairly new manager, however, based on my research most of the experienced managers seem to recommend prioritizing HQ upgrades in this order:
1. Design HQ - so you have more design points to allocate after each race
2. Technology HQ - so you have better DRS and longer KERS
3. Manufacturing HQ - just enough to sustain parts required for your car repairs.
Once these have been maxed out, you can go for youth academy and/or simulator HQs.
Most people agree that office and hospitality HQ does not seem to have an effect in the game at the moment, so this is the last HQ you should focus on.