A better player would give you better advice than I can
But glad to help if possible.
That looks like brutal terrain. Seriously, just install the Acken and Hellblazer maps. You might pick up bad habits from playing on bad terrain.
I believe that better players are capable of managing the WHOLE game -- by which I mean that they can keep track of multiple areas of concern at the same time. They can multi-task, and don't lose sight of one thing while dealing with another. So while they are building their army and their science, they are also dealing with diplomacy, and so forth.
And on that score, it helps to know your enemy. This is one area where I am poor. There is a table somewhere on the forums with the leader characteristics in numerical form, so you can learn who is likely to be aggressive, expansionist, etc. It helps to know that Dido is always treacherous, and will befriend you then attack you for nothing. I point this out, because one of the skills you need is managing diplomacy. If you know that a Civ is going to attack SOMEBODY, then you make sure it isn't you. You do this by husbanding resources and paying bribes. And if you are planning to attack someone yourself, it can be good practice to make them a hated warmonger so that you get kudos for destroying them. You also have to bear in mind that the AI is programmed to make use of its advantages, so an AI that gets its Unique Unit is much more likely to go to war. So as soon as Rome gets Legions, be prepared for it to attack someone -- preferably someone else, because you have bribed them. Warmongers can actually be great neighbours because they may attack others for very little. If you have two neighbours who are likely to be aggressive, like Rome and Sweden, what could be better and more attractive to them than fighting each other
Or if you are already fighting Rome, Sweden might think it is a good opportunity to join in, because Rome is already "busy" and therefore more vulnerable. You need to be as nasty and duplicitous as they are
Sending caravans is important, because it will give you a positive diplo modifier, and so is trading. Sell everything you don't need -- horses, iron, luxes. Don't think "I might need those horses later" -- sell them. If you have six horses it will take you an age to build all the horsemen that would use them up. Also remember that caravans may give you more science than a library to begin with. In some circumstances it may be worth settling in a spot that will allow you to leech science with a caravan, but you have to balance it against other factors. In other words, it might be what decides you to choose one spot rather than another that seems equally attractive.
That's what I'm hoping, anyway! 
