Do I need HQ for boarding squads? Or is it better to just not bother at all?
There is no such need.
Normal boarding squads are small, and even a minimum-size HQ will take remarkable portion of their tonnage, and so even if you find some very good officer with relevant skills - it will be hard to outweigh, and in addition, these squads will be in this case a killer-traps for these good officers, because there is no such thing as rear echelon during board combat, and it might be some level of boarding-drop casualties.
Though if you have large boarding squad to take large enemy stations and immobilized large ships - then HQ might contribute well with acceptable risk.
The absolute minimum size for an HQ is 10 tons assuming an infantry base type. For a small (say, 250 tons) platoon I would agree it is not worth it, but a larger company-sized formation of nearer to 1,000 tons it can be good value. You can even at this tonnage double up (20 tons) to improve survivability, but generally for such a large boarding formation the casualty rate will be very low simply because the kill rate will be very high.
Do garrisons need logistics units?
Whats a good rule of thumb to determine how much logistics a force should have?
They don't need them but they can use them.
LOG modules
only matter for direct combat, i.e. when Army A is shooting at Army B. For day-to-day sitting around on a colony breaking up bar fights and arresting petty thieves no GSP is consumed or needed. However if your garrison gets into a fight they will probably need LOG modules to last long enough against the enemy - however, if you have a 5,000-ton garrison and the enemy lands 500,000 tons of troops logistics will be the least of your concerns.
There isn't a good rule of thumb, but in general the amount of logistics a formation requires is enough for ten rounds of combat (one round is 8 hours). So what you really need to do is work out how many forces are involved, estimate what kind of kill rate you expect, and then based on that work out how long you expect combat to last and embark enough supplies to resupply your formations for that many rounds.
As this is a lot of work, my rule of thumb is "a lot".