If I build no engines into them, how will I be able to first strike? The DL can just outrun me.

Duck and then strike hard with the appropriate tech. Early on, use a few really fast ships trying to take ot their transports. Large ships can hold an engine and enough plasmas to take out first DL fighters - later frigates with a single salvo. It is pleasing to see a Destroyer taking out ship after ship. On normal the DLs are quite late with logistics.

What approach?

I have a follow up question:

How exactly do military resources work? I built a full mining starbase (+19) on one resource and my ships gained 25% attack (from 18 to 24). I then built another base on another resource, but that didn't change anything.

Galactic resources work by increasing your Ability bonuses. Economics, Influence and Research are self-explanatory. Military resources, however, increase both your Weapons and Defenses abilities. All of those bonuses work as a percentage. So, if you have no base Weapons and Defense abilities, and your Military Mining Starbase grants a +19, the weapons and defenses of your ships will be 19% more effective. I don't know how rounding works in this case, though.

In regards to the second Mining Base not doing anything, it is very likely as LTJim said. So, make sure it really is on a Military resource (double-click on the base and see what kind of bonus it provides). Another possibility is, that the bonus from the second base is just too low to make a noticeable change. Especially if the base strength of the weapons on your ships is also low.

Okay, remember that I did warn you!

REPEAT!  SPOILER EXPLOIT WARNING!

Before I start, be advised that it works best if you have high intel level, though it is not strictly necessary.

The corral approach is based on the AI near-inability to change target so long as the existing target continues to exist.

You get an AI ship or fleet chasing (or seen to be targeting) a ship or something.  Next, you bring 8 ships -ultra cheap is fine! - into its path and englobe it.  It cannot move until it re-targets one of the 8 posts in its "corral."  Meanwhile, ship #9 loiters nearby thumbing it pixel nose.

The same principle can be used in reverse to protect mining starbases.  That is, put your own base in a corral of 8 ships.  The AI cannot target the base until it removes a corral post.  Again, a 9th ship is handy (along with high intel) because if the AI targets a fence post, you rotate the targeted ship onto the mining base square and put a new ship in its "post hole."  Again, the AI cannot retarget.

IIRC, one can also englobe/corral a target planet.  Again, IIRC, no ship can be built/launched when there is no free square into which it can be launched.  This makes invasion easier and, when you finally capture it, the planet will have gobs and gobs of shields ready to be used instantly as a present!

Note that if you do not have the 8 ships, as long as the AI speed is fairly low, you can make a wall of 5 or 6 and frustrate the AI ship/fleet indefinitely by playing keep-away with your ship going "through" the wall and the AI condemned to forever be going around it, unable to catch it.

Once, as a test, I walled off half the map with cheap ships, kept a few post-replacements handy in case a post got targeted, and the AI never crossed it.

Another time, I "herded" a particularly nasty AI fleet via parallel lines straight to the planet of another AI with which it was also at war (but I was not).  The second AI put together a fleet and I graciously "opened the gate" and watched the battle!

IIRC, the defense value of the "wrong" defense is the square root.  That is, a 100 shield rating = 10 armor or 10 anti-missile.  Meanwhile, each attack is "rolled" separately and is a random value between 0 and the max weapon rating.  The fleet is not a combined roll.  Since one ship can kill multiple others in one battle "turn" even each individual ship may not lump all its weapons into one combined attack.  There have been multiple threads on this over the years, so you could look or ask about this.

Thus, if your individual gun values were small enough per gun or per ship, each separate attack might not have gotten a die roll to exceed the DL's adjusted "armor" defense rating