Weapons - as long as you always attack first!   

Speed
Sensors
Soldiering

The three "S's" of SucceSS

I would pick speed. If you have speed you can avoid battles that are unfavorable to you and strike targets of opportunity of your choice.

Fast fleets are also useful for intercepting enemy fleets on their way to invading your planets or taking out your mining starbases.

I would convert your startegy based on what planets and resources you have at your disposal. If you have a lot of military and econ resources conquest is your game since you will be able to sustain a large army, if you have nice pq planets and good research bonuses maybe the middle path of research and war, if you have a few influence and you get ahead in diplo techs start culture bombing. With anything but conquest i recomend researching weapons/engines every 2 - 3 other techs just to stay in the power game and not be considered a quasi-power by the other empires.

I always use the stratagy of big, expensive, quick ships. They take a while to build, and are only worth building on a few key industrial planets (due to the time involved). I usually will have certain planets that I will rally the fleets to, then have the fleet cover between two to four star systems (which is why speed is neccesary) along my empires perimiter.

I figure that the best defense is a good offense, so even if I am not attacking, I use the fleets to intercept anything coming in before they reach my planets.

I usually play on gigantic galaxies, with rare stars (tight clusters), and aboundent on eveything else (it gives it a big empty space feel), so I don't have a whole lot of planets initially to maintain huge numbers of ships (if I have a hundred ships then I am usually stretching my economic limit). So, the smaller fleets are good for my economy.

The size of ships that I use are:

Tiny- At the startup, they are cheap and quick.

Medium- My next step up from tiny, form my intial backbone, and it is here that my fleet stratagy really begins to come into play.

Huge/Massive- Once I have this I stop building mediums and switch over.

It's hard to go wrong with fast medium ships with no defenses and decent weapons. They're fast to research and cheap to build, and plenty effective against almost anything.

I'm not sure I understand. What good are fast ships, if they're too weak to actually do damage to opponent fleets?

Edit: btw One "cheese I've heard about is pile a hull with engines, get it across the galaxy, then upgrade to heavy attack mode. Kind of like having transformers. Car mode=speed/Robot mode=attack

That can be awful expensive cheese. This could easily cost 30K per ship. It can be done but why would you bother?

.... if it weren't so expensive.... dang! thats friggin ingenious!