First of all: Wellcome to the forum, both of you.
Here are some random bits. All is just my humble opinion and not set in stone:
* Don't listen to the mouse. WP's are useless early
* It should be possible to pull your setup off without mines, but if you do want to use them: Research mines (I) first.
* Forget about missiles.
* Fighters are very effective against some of the AI's, but not all of them. If you use them, use large stacks only.
* Don't build (and pay maintanance on) useless ships. LC's are IMHO the first usefull beam ship(sorry Rex
). Only usefull weapon for smaller ships are Boarding parties.
* Early important Research: Mines, PDC (III), Boarding parties, Ships up to LC, PDC (IV or V), Armor (III), Training. CS and ECM can be retrofitted and should come as soon as posible after you have the tech to build "real" ships.
* Get your ships and fleets trained to the max ASAP.
* Don't waste early research on useless stuff like Propulsion (II or III are OK if it helps you get those colonizers produced faster), Shields, Research II and Minerals II.
* Don't panic, don't fight loosing battles if you don't have to: Fall back instead, watch your happiness (build troops if you have to).
* Choose the time and place for the major battles yourself. Its better to fight with your full trained ships midsystem, than with half your untrained ships at WP.
* If you do fall back, it will usually create an oportunity to slip some raiders behind enemy lines. Sneak them in and bLast away, some of the better offensive AI's will crumble quite easily when their planets dissapear.
* The AI's are stupid, and do follow set patterns. Think out of the box and you should do OK