there are so many variables to give you any "right" answer.
What works on Begginer is useless on Tough, what works at tough will fail at Suicidal.
Your race set up can have a big impact in this are as well. Your choice of Political party for instance can have a huge affect on the game, as well as what racial bonuses you have picked.
What some of the basics are though is a solid economy fuelled by measured expansion and high morale.
Early game try and focus on getting you population to grow. Do this by keeping your approval rating as high as posible. 100% approval will give you a 100% bonus, but if you can keep it green as long as possible your population will increase and therefore your income.
Try and research as much as possible to attain a tech advantage. This will kepp you out of trouble should war come.
I'm sure you knew most of that but those basics are good for all levels of the game.
The main thing is everything just happens alot faster on the harder levels. the bonuses the AI get allows them to colonize faster, research faster and ultimately produce a military faster than you.
One thing i do is to only colonize a set amount of planets. That might be 10 or 30, depending on the galaxy size. Over extending yourself will hurt you.
Specialize your planets. Make your HW your Manu Cap and fill it with factories, pick another PQ 10~12 planet as another production world. Pick say 2 or 3 planets to be your research worlds and place your Tech cap on the biggest of those.
Then try and make all other planets econ worlds. Once you have the money rolling in you can do just about anything, and these core planets will fund your expansion.
Ignore the low PQ planets for the first few months. Even if the AI takes planets near your HW, you will flip them soon enough, concentrate on getting the PQ12's+ in your vacinity first. Build these planets up and then work back toward your HW grabbing everything in sight.