I've seen some great advice on how to play certain factions and was hoping to centralize it to a single thread.
edit: I'm just gonna add quotes
Imperial Remnant
I like to concentrate on military and get the Strike Cruiser researched ASAP. Start building them as the backbone of your navy, while concentrating on your economic research. Get the increased taxes researched first, this is your major income booster as the IR (and make sure to start getting your planets that can have high populations researched to allow those populations to grow and get the income).
Once you have some good income, research your weapons improvemnts, and then get enough economic stations to do the research that gives you free supply/command. That's huge, and will sustain you for a bit without having to deal with upkeep. Once that's researched, go hard and heavy on your military research.
Dreadnaughts will be one of the other backbones. They're super cheap, requiring no tibanna, so you can build them very fast, and they have pretty good damage. The Strike Cruiser carries a bomber or an interceptor, but comes into it's own once you research denting strike. Once that's researched, you want a lot of Strike Cruisers in your fleets. Ton Fauks Falks, whatever, are the best way to get a lot of Scimitars in your fleet. Victory I & II's can carry them, but they're expensive, cost a lot of fleet, and only carry 1 per. The Escort carrier carries 2 for about 1/2 the price in resources and supply. The Victories will be the "heavy hitters" of your non-capital ships. You need a good quantity, but realize that going overboard sucks up your supply like crazy compared to Strikes and Ton Falks. The MTC is an awesome ship. While not cheap, it's not insanely priced, has decent combat ability, can carry 2 squads (with their ability), and can restore fighter supply in the middle of combat without worrying about IMMEDIATE destruction. While they don't do hull repair, they lifesavers for a fleet you want to keep on the move.
ISD-II's will be the bulk of your capital ships. Better in every way than the ISD-I, except they can't capture planets. A few Allegiances are good, but don't go overboard. Their size makes them slow, and their abilities make them a bit suicidally agressive.
New Replublic
For the NR, my preferred strategy (on non-Hapan maps) is to rush the boarding party tech ASAP and start grabbing garrison Dreadnaughts, Strike cruisers and VSDs right away. Almost for free you can end up with a ton of heavy cruisers in the early game, speeding up your expansion and giving you an edge for early battles with enemy fleets. It'll require a fair bit of micromanagement and getting used to using boarding party effectively, but it works well.
I forgot to mention that one is going to need Hajens very quickly to make this strategy work effectively, and they too are best micromanaged - turn off fighter resupply auto cast (conserve fighters by keeping them docked until Lancers are taken out), and it is also best to turn off repair auto cast. You only need to get captured ships up above 50% hp for them to be at full effectiveness, and maintaining supply and timers off guarantees you the ability to get them there fast.
With the NR, one of my favorite strategies is to play defensively. Get as many planets as you need to easily get your economy growing, build up massive defenses along your borders, build 3-4 moderate sized fleets to patrol your area, and make sure everything for culture is researched, and build the $@^& out of culture centers. Once your culture has pushed the enemy off a planet, combine a few fleets into a giant attack fleet and destroy all the infrastructure they left behind in the planets gravity well, and build it up as yours. It's not pretty, it's not fast, but it irritates opponents to no end to throw their fleets at you to die trying to destroy your culture centers to protect their planets.