The United Empire is a good beginner faction, so stick with them. They are a straightforward defensive faction which is good at making tons of money, their ships get lots more hp and their planets are hard to capture, so you'll have a few extra turns to react.
The first thing you should know is that, out of your starting heroes, if any of them are Administrators (gear and wheat icon), hire them and stick them on your systems. When they level up pick Labor perks, and anything that gives +industry or +food. This will get you started well. You should also drop your taxes until your empire happiness is "Fervent" (80% or better). Since you are the Empire you will be making money anyway, and this will provide massive research, industry, and food bonuses to all your planets.
Unlike many 4x games, if you expand too fast your people will hate you since uncle jim is eighty light-years away. Capture only the best planets, in six or so systems. The best planets are jungle, terran, and ocean, arid and tundra are second best. If a planet has a positive anomaly on it like Rich Soil, Low Gravity, etc., then those are better. The reason why those planets are the best to colonize early is they make lots of food, and the higher your population, the more of everything you'll make. The best systems are ones that can support HIGH POPULATION. Try to get systems with lots of planets in them, even if only one or two planets is any good, later you'll be able to terraform the others up to snuff and make a real powerhouse system out of it.
So in short: Early on you should colonize...
1: Terran, Jungle, and Ocean planets, Arid or Tundra planets if those are all that's available
2: Planets with special bonuses or resources.
3: Systems with many planets in them.
4: Don't colonize (until later) planet types that give more than a -10 penalty to happiness (lava, barren, gas giant, asteroid). If the planet has a positive anomaly that adds happiness, that can make it good.
5: Don't colonize too many systems right away, due to expansion-based unhappiness. Six is a good solid start.
So now you've got some good systems. The first thing you should build on any system, no exceptions, is the Heavy Isotope Refineries improvement. Early on your systems have crap population, so you want improvements that give a flat bonus regardless of how big your population is. The isotope refineries will give you a flat bonus to industry that will let you build other stuff and actually get productive. Fortunately you're playing the UE, so you start with the heavy isotope refineries research unlocked for free.
The second thing you should do is build a planet exploitation on your colonized planet. I highly recommend the food exploitation. More food means faster-growing population, and high population improves production of everything. Once your population caps out you can change the exploitation to industry or whatever you want.
Your first three researches willl probably be Soil Xenobiology, which makes your food exploitations better, Arid Epigenetics, and Xenobotany so you can claim those arid and tundra planets. Unless you're playing on a very small map or have lots of enemy factions, you can ignore military research for a while. More on that later. After you get those three, look around your empire and if you have Redsang, Bluecap Mold, Dustwater, or Hydromiel resources anywhere, take a turn or two to grab the Xenology research so you can make use of them. If not, then skip it and beeline straight for Nonbaryonic Particles on the right-hand side. This unlocks access to some really good luxury resources, but the real reason for getting it is it unlocks the Magnetic Field Generators. Build these in all your systems as soon as you can. They crank up the research in that system by a massive +40 research points per turn, regardless of the system's population. These will catapult your research into the midgame tier. Once you've got that tech, get Core Mining and High-Energy Magnetics to improve your industrial capacity.
So a good early research order in short:
1: Soil Xenobiology
2: Xenobotany and Arid Epigenetics
3: NONBARYONIC PARTICLES
4: Core Mining
5: High-Energy Magnetics
So now you've probably met some other empires and from here it's harder to say what's an optimal build. If you've got more space to expand, grab the Botanical Scanning tech to build supermarkets and offset the happiness penalties. If you started next to a belligerent faction, head for Flawless Machining and Efficient Shielding to make laser destroyers before they are likely to have any shield techs researched at all. If you've got some good-looking planets in your existing systems, get the techs to colonize them (make sure to maximize food production to fill up the new population space.)
The galaxy is your oyster!