A one word answer to all 3 questions is: depends
Unfortunately, it really does. There's no best way to start, and it depends a lot on the map and who you're playing against. For example, setting up a good economy, with trade stations and such, slows down your early military production and takes time, both of which are bad if you're playing a very small map. Unless your opponent is not focusing on military, if you spend too much on economy and not enough on military, you're going to get squished.
In general, though, you want to expand as quickly as possible. Scout early and scout far, leave your scouts in systems you know your opponent has to go through so that you have advanced warning and can see his fleet makeup and hopefully have time to gather a proper defense/interception, or just hit his undefended planets instead. Research, in the early game, sucks a lot of valuable crystals, which are gathered slowly until you get several crystal mines under control. So, in the early game it pays off to research exactly what you need and nothing more. For example, if there's a volcanic or ice world within 2 (maybe 3) jumps of your homeworld, it's best to save enough resources to research ice/volcanic colonization ASAP because both planet types are very beneficial and sought after. But it makes no sense to spend the resources researching either if there's no immediate need for it.
As for military, only your capital ships gain experience, and in that regard avoid sending level 1s into battle as much as possible. If you can spare the credits, train them up to 3 before sending them to fight, they'll be a lot more effective. Numbers usually don't mean as much as ship types, but they are important. If you know your opponent is slacking a bit on military production, you can focus on it and have an advantage, though it's risky because if your fleet is defeated, it'll take you longer to rebuild because your economic infrastructure isn't too developed.
So, as you can see, it really does depend on a lot of things. The best advice I can give you is SCOUT. You need to know what your opponent is doing, and develop your own empire accordingly
