Also, once you start winning a war you will likely get advanced techs from somewhere down one or both of the other two weapon tech trees. Which means you will not have to research them or any techs preceding them (don't ever research weapon techs that have already been 'bypassed' unless you actually _want_ to build the lower tech weapon for some reason). So for instance you can research to Doom Ray yourself then go to war against a missile empire and steal Quantum torps or whatever and be only a couple techs away from Nightmare Torpedo having done absolutely no expensive missile research!
The tech and costs always seemed backwards to me. Seems like missiles should be _lowest_ research cost but highest cost (thinking re-supply here, so maybe maintenance would be more like it but you do not pay for actual weapon mount maintenance just for your ship hull, right?) to actually build, with beam the opposite and guns in the middle. But I guess that is my own mind's universe.
It does also take some amount of time for the AI to counter your first weapon choice. If you kill somebody off and do not just skirmish with them you will probably find you can get most of the way thru the war, even on a large map, without the AI having the ships out there adjusting until near the bitter end (maybe it is because I usually do not build warships until the war starts but set up to build them very quickly after it does - if the AI adjusts to your actual ships and not your tech ability it might never know until the war gets going and then faces a time lag, plus often it is also at war with another AI so has to split between defending against their weapons and defending against the player's weapons). It is sometimes the _next_ AI empire that poses the problem. Even then, if you are really loaded up the AI just never in my experience puts enough emphasis on defense to make a huge difference, preferring weight of numbers. But yeah it does make it a good idea, once you have reached the end of a weapons tech branch, to shift your tech down another line especially if you have a leg up due to some stolen techs from successful invasions.
Not sure wether or not it is economically best to retrofit your existing ships tho, someone might want to crunch those numbers. Sometimes when I hit that point I am well past where the AI can stop me militarily anymore. But I do not play on anything higher than 'tough'.