You might try looking at these (if you haven't already):
[url=http://strategywiki.org/wiki/Master_of_Orion_II ]MoO2 on StrategyWiki[/url] (this is mostly concerned with muliplayer games - you may not want to pick "Repulsive" as much in single player)
really useful FAQ another FAQ I've found the game is easier when playing a custom race, rather than one of the stock ones.
Regardless, you want to make sure your earliest research includes Research Lab (this is the first thing I get if not on Pre-Warp) and Automated Factories. The research and production boosts for those are vital in the early stages. Planetary Supercomputers is another good one to get quickly. After that it really depends on the race you're playing - for example, high pop races (Subterranean and many Tolerant ones) may want to head for Soil Enhancement to keep everyone fed (and free up population for production/research).
If you have other decent planets in your home system, it's a good idea to colonize those as well. For that matter, a system with two or more planets is generally a more attractive choice for colonization than a single planet system. You can use colony bases to grab the other ones, and it's much easier to defend say, three planets in one system, than three planets in three systems.
In the beginning, you'll want to keep 1-2 guys producing (colony base, colony ship, battleship - anything that'll take a while to build) while everyone who isn't farming researches. Once you've got a new building (like the Research Lab), put it on top of the build queue. The production that's been built up will transfer to the new item - often this may mean it's finished in one turn.
Scout every planet you can reach to find the best place to colonize. Never send a colony ship to an unexplored system. Scouting can also give you bonuses if you're the first one to visit a system (marooned leaders, money, tech from Artifact worlds). If you get Battle Scanners, it's not a bad idea to refit your scout design to include these, as the scanners increase detection range. I often keep one or two scouts out at my maximum range; with luck, they'll allow me to spot alien ships before I've come into contact with them. It's very useful regardless of whether you want to make contact or avoid it.
Armor is really useful. I can't count the number of times I've slaughtered AI fleets because they were still using Titanium armor in the mid to late-game. Usually, I go for Zortium after getting the stuff mentioned above.
The weapons I use vary, but generally early on I'll rely mostly on frigates and maybe destroyers armed with MIRVed nuclear missiles. Those may be back up by a cruiser or battleship armed with lasers (you'll want Battle Scanners on those). After that, it's usually Fusion Beams or Neutron Blasters on the heavier ships. The smaller stuff will get either MIRVed Merculites or Anti-Matter Torpedoes (once I can put all the mods on those). Sometimes the Battleships will be armed with torps as well - depending on tech and what special equipment you include, you can cram from 5-7 fully modded AM Torps (plus some point defense fusion guns) into a battleship hull. It's like throwing sledgehammers at people :)
Another interesting way to outfit a ship is with Neutron Blasters plus Transporters. Kill all the marines on the target, beam aboard and just capture it. Those are great for stealing tech (and scrapping 'em gets you extra cash). I may still put an anti-matter torpedo on those for the extra firepower.
If you haven't seen it, there's a thread on
Early Weapon Design that ought to be useful.
On the Diplomatic front, never enter an Alliance unless you are dead certain you have no chance of surviving without it. Your "Ally" will often drag you into wars, then make peace with the yahoo he asked you to attack. :P Tech trades are usually a good idea, though you should never,
ever trade stuff that gives a Spying bonus.
Hope that's of some help.