As far as the TEC starbase goes (and for most cases, Advent as well), it depends completely on whether you're up against AI's or humans.
The AI will mindless throw its army against your starbase, whereas a player is more likely to try to move around it without engaging it directly. This fundamental difference in approach means that how you use your starbase is difference. Against the AI it's a bulwark that stops their advance. Putting it close to the edge of your gravity well (right where you expect them to warp in) and then covering your other flanks with mines is a great approach. This is what the AI does most of the time.
A player (at least a smart one) will look before he leaps, and is likely to go around rather than trying to go through your starbase. You can't simply presume your starbase can block the enemy completely, so instead of treating it like an impervious barrier it's better to treat it like a speedbump, something the enemy fleet has to maneuver around if they want to get past it.
Typically there are three positions I put my starbase: front-face, rear-facing, and planet-side. A front-facing starbase is where I expect my enemy to warp in. While a player will still move around this location, this means their angle of approach into the gravity well is quite predictable and I can place my defenses appropriately. The second position is rear-facing. This position is to try to prevent the enemy from going through this gravity well and into the next. This method is designed to maximize the amount of time the enemy fleet has to use to get around your defensive line and into your next gravity well. Using it combines a PJI or two with lots of static defense. The final positioning I use is planet-side. I typically do this when I need to protect my valuable civic structures in a gravity well I could lose. By clumping all my defenses (including the starbase) into a tight ball, I can protect those civic structures and ensure their survival even if the planet is taken.
I find starbases are best placed in small gravity wells; neutrals and asteroids work great. This is because there is a lot less room to maneuver and the starbases weapons can cover a lot more of the area of the gravity well. This makes them harder to maneuver around and all the more powerful. Choke points are obviously good places to put a starbase, and typically putting up some repair bays within range of it is also a great idea (starbases regenerate health notoriously slowly).
I personally believe the TEC starbase is the worst of the three, and the Advent is only better once it has its late-game meteor control upgrade. The Vasari starbase is the only one I'd bother getting early or in considerable numbers.