Make dedicated siege ships - either with manpower modules or titanium slugs (depending on whether you have more titanium or manpower). Use the defensive T1 hulls.
Military quadrants give you better weapons, but you have to equip them. You can usually tell the tier they're on by looking at the icon ie. T1 missles have one rocket, T2 two, T3 three.
Strategic weapons are often not worth it. Build two normal ships instead of one with bigger guns.
Learn to micro pops - you want Modernization 1 for spaceports. Spread minor faction pops that give you good bonuses (industry primarily). When you have 20 you usually get some percent bonus - having just one pop in a system will apply it. I usually make a "prison" world or two for the pops that I don't want the bonuses of. Pop micro is also something that Horatio needs and he's one of my favorite factions.
Overextension is a soft cap - you usually WANT to go over the limit by one or two systems.