For the most part, arming starbases simply isn't worth it. There are exceptions, but beyond early to mid-game techs, a starbase simply cannot have enough weapons or defenses to hold off even a moderate enemy fleet. Keeping a fleet nearby to defend is almost always cheaper and more effective, and can be moved to other threatened areas at need. Modules on your base cannot.

One absurdly cheesy tactic you can use is build dozens of one weapon tiny hulls and stack them *unfleeted* on top of your unarmed base. Enemy ships will wasted one move to kill each ship before they can attack the base, giving your real fleets time to react.

It's not about the weapons actually on the starbases, it's about the assist modules.   All your ships within the military starbase's sphere get beefed up by the assist modules.   Particularly, it's that "Protective Fields module"--the one that gives your ships +1 of each type of defense.  You have to have at least 1 defense in something on your ship to start with, or you won't get the bonus.   To make a really long story short, it's like getting +3 defense on all your ships.  That's a big deal, when you're first starting to put out fighting ships.

To take full advantage of them, build the Tiny ships, but DO fleet them, and when you do it that way I do NOT consider it a cheesy tactic.  It's legitimate use of military SB's.

Also, military SB's are NOT solely a defensive weapon.  You take along a fleet of constructors with you, just as if they were transports or fighting ships.   You build your SB right as you're about to mix it up (thus guaranteeing that your SB will be used at least once).   Then your military SB becomes a defense for your NEW-found planets, along the NEW borders of your empire.

Consider the economics of it:  the key here is that, because they are ASSIST modules, the military SB does not do any of the actual fighting, and thus does not normally die in combat.  All the Tiny hull ships you sent in do.   So at the end of combat, you may end up left with an immovable, possibly un-reusable starbase, but that's a heck of a lot better than a bunch of dead, expensive ships.

This effect is more pronounced earlier in the game (because of Protective Fields), but take the high-end of the technology spectrum:  assume that everybody's researched a bunch of weapons and all of the Starbase assist techs.   Without going into all the details and what-if's in my calculations, generally speaking you can build a pretty kick-butt military SB with 17 constructors, which will boost your Tiny ship from 1 Attack/1 Defense to 33 Attack/6 Defense.   A good middle-of-the-road Tiny ship will cost around 60bc; a constructor will cost exactly 95bc (Tiny hull+constructor module = 25bc+70bc).  Maybe tack on 4bc for life support.  Let's do the math:

Cost of 20 constructors (I'm throwing in an extra 3 for little knick-knacks like Speed Assist modules):   1900bc.

Cost of a fleet of 10 Tiny ships:   600bc.     Unassisted:   10 Attack/10 Defense/80 hit points.  Assisted:  330 Attack/60 Defense/80 hit points.    Note that these numbers are all pre- any civ-wide military bonuses. 

You can, potentially, build a single Huge Hull ship with about the same stats (330A/50D/80HP), but--for 600bc?  That's unheard of.   It will cost you closer to 2500bc:   the price of the Tiny fleet and all of the constructors combined.   So in terms of cost, you are reaching your break-even point after just ONE fleet of 10 Tiny Hull ships.   I would never do all this just for one fleet--if I'm going to all this trouble, I'm sending in 3 or 4 fleets, plus some bigger ships (whom I don't intend to die), and there's some epic set of battles about to happen (it is only intuitive that you would set this up in a war zone, lots of battles).   30 Tiny ships:  that's almost 1000 attack plus 150 defense that starbase is conferring.  At a price of a whopping 1800bc (plus 1900bc for the starbase).   And this is all pre-bonus.   You just can't achieve this level of economics by building starships straight-up.

There's only one catch in all this:   some of your Tiny ships WILL die.  No big deal.  They only cost 60bc.  I can lose an entire fleet of them, and I'm only set back 600bc.  Other guys will lose a Large Hull for 2.5x that without blinking.  This is where the advantage of the assist modules kick in:   I am not actually exposing the starbase to combat.  It doesn't die--the cheapo Tiny hulls do.   Where other players try to get around this is by building invulnerable ships, i.e. very-high Defense, high Attack with Super Warrior ability, or by way out-teching their enemies.   Now if you're able to build invulnerable ships, obviously that is going to be better than losing several Tiny ships and burning 1900bc on an immobile starbase.    But I consider that a sign of playing at too low of a difficulty level--if you're able to go all game with invulnerable ships, your difficulty level is probably too low.   The AI should at least be strong enough to inflict some casualties on you.   And when he is, this is how you beat him, dollar-for-dollar.

The only time I've ever won a tech victory was as the Altairians in DA.

The only reason I did it, was to just say I did.

Got five high PQ worlds decked out with nothing but labs, and I just waited (for a great many turns).

I usually give a starbase at least the most basic weapons, that is +1 in all 3 categories. This is just so some defender ship can't get in and kill a starbase, but I don't try to guard against large fleets or ships and I don't ever really get around to reseraching the techs either. I use fleets and individual ships to defend star bases. The AI will usually go after your stabases right away so its not a bad place to keep ships anyway.

As for military styarbases, I like the idea and I always want to build them but I bnever get around to it. The don't move and the amount of time that I can expect battles to occur in their area is small. They do have the added benefit of havinf the plus and minus speed modules, these can help you no matter where the fight is if you place them right. Since I like to play as the Yor, their superability of 3 speed for all enemy ships is a great defence. Now couple that with a -2 speed for enemy ships and you have invaders traveling at 1 space per turn. Now, add THAT to the above strategy and you have but one cheep ship lost per trun. You can replace it faster than the AI can destroy them, since the AI wouldn't think to un-fleet to get more attacks per turn.

What a few people do to get massively high scores is to build a military starbase array around a point and fill that ponit with ting hulled, 1 attack ships. Mumblefratz had a post where he showed the placement of the starbases. Basically  your one- attack ships becomes very powerful with all the added weapons multiplied buy 1000's of ships.

It looks like the days of high-score cheese and Spin Control with military SB's are over in ToA.   And you have to have Hyperwarp to get the -1 Speed Modules.  That tends to rule out the majority of the game (let alone the part of the game where you haven't already won).

It's a small consolation, but with offensive starbases you can use them to help interdict the AI planets' orbiting ships as they pop up.  Say the AI is more powerful than you, and he's got a system of 2-3 planets a quadrant away.  Hopefully he's got 4-5 fleets in the area as well.  The offensive SB strategy says, send in a fleet of constructors along with some Tiny hulls and fighting ships.  Possibly research Starbase defenses in transit.  Note that I did NOT send in transports.  No time.  It's a matter of priorities.  Build the offensive SB right as you're about to do battle, engage.  Then, you get the SB's assistance as you take out his orbiters.  This is where Protective Fields can help you a lot if it's early enough in the game. 

Now at this point, I can just send in my transports whenever it's convenient.  Usually I will hold out for Adv Troop modules here, so all those same planets of mine who made 95bc Tiny-hulled constructors can turn around & make 95bc Tiny-hulled Adv Troop transports.  Why rush it?  You own the airspace.  The "strong" AI will be spinning his wheels creating new Defenders, only for you to blow them away the next turn.  He may even send in a fleet or two--which is EXACTLY what you want.   A few months later the transports arrive (maybe research Planetary Defenses and build Tir Quan in transit), steal some techs.  You may even hold out for an influence flip--I've had that happen.

Your offensive SB now suddenly becomes a defensive SB, defending your NEW perimeter.  Which works out, because those new planets have <1B population and are a little vulnerable to counter-invasion.  Those captured planets can even build/purchase their own Defenders right away--the Tiny hulls only cost 60bc.   The +1 speed module usually fits in right about here--it tends to help you the rest of the game, because using this strategy the military SB tends to get located right along your rally points and trade routes.  Just kind of works out that way.

An alternative strategy is to send an extra constructor along with your initial fleet and add the +1 speed module right up front.  It can help, because those Tiny hulls don't have engines.  But usually I will only try to do that if I'm picking the fight (often I'm doing all this because the Drengin/Korath declared war, they're way ahead of me, and I don't have the time).  But if you are picking the war, this way is nice, because the AI doesn't deem your constructors a threat the same way as if you sent in a bunch of transports on the first wave.

I now wish to take this opportunity to thank the AI for their gift of Stinger III to my civilization.  My agents really appreciate it.