That's a rather broad question. First off, I'll point you in the direction of some of my game writeups, which should give a good feel for the kinds of paths I tend to pursue. Plus you'll probably hear a fair bit about this sort of thing in the SG once we get started. 
Here's a wiki page with links to several game reports, the ones on this page are all good reading. Mine are at the bottom of the page. (There's more to be had in the Kerberos TAR forum, some better than others.) There's also several links to posts designed to help new players, and the wiki itself is of course a great resource.
http://sots.rorschach.net/Strategy_And_T...um_Archive
Now, regarding tech paths, there is no one magic formula, as it depends greatly on what race you are playing and what your situation is in the game in question. Each race is more likely to be able to progress in certain fields rather than others, and your situation tells you how much you should be concentrating on guns versus how much on butter.
Generally speaking, though, technology is not nearly as important as many new players assume, especially at the start of the game. What is really important is economy, because that's what drives everything else. So near the start of the game I tend to de-emphasize tech while I am busy getting my initial expansion effort going. Early game is all about the land grab and making sure you have a viable amount of territory to build from; I tend to research only what I need for minimal self-defense (a small mount weapon and CnC) and to maximize my expansion effort -- mainly this means early industry/drone techs, certain biotechs, possibly power/drive techs, and eventually FTL Economics for trade. While I'm doing this my military goals will be focused on scouting denial and raids on weak targets of opportunity more than full-fledged assaults on enemy strong points.
Later on, once I have a well-developed freighter network and many colonies to trade between, I'll have plenty of money for researching all the cool toys. That's when I start looking to invest in the techs and ships needed for a serious warfleet to start kicking my rivals' teeth in. What weapons I choose for my initial warfleet will vary from game to game depending on what race I'm playing and what I feel like using that game. Once I've got a couple warfleets put together, I'll start sweeping up a bunch of nice-to-have cheap techs I likely skipped earlier and also grab megafreighters, then I'll start working towards either stations or upgrades for my fleet if I need any.
Here's a wiki page with links to several game reports, the ones on this page are all good reading. Mine are at the bottom of the page. (There's more to be had in the Kerberos TAR forum, some better than others.) There's also several links to posts designed to help new players, and the wiki itself is of course a great resource.
http://sots.rorschach.net/Strategy_And_T...um_Archive
Now, regarding tech paths, there is no one magic formula, as it depends greatly on what race you are playing and what your situation is in the game in question. Each race is more likely to be able to progress in certain fields rather than others, and your situation tells you how much you should be concentrating on guns versus how much on butter.
Generally speaking, though, technology is not nearly as important as many new players assume, especially at the start of the game. What is really important is economy, because that's what drives everything else. So near the start of the game I tend to de-emphasize tech while I am busy getting my initial expansion effort going. Early game is all about the land grab and making sure you have a viable amount of territory to build from; I tend to research only what I need for minimal self-defense (a small mount weapon and CnC) and to maximize my expansion effort -- mainly this means early industry/drone techs, certain biotechs, possibly power/drive techs, and eventually FTL Economics for trade. While I'm doing this my military goals will be focused on scouting denial and raids on weak targets of opportunity more than full-fledged assaults on enemy strong points.
Later on, once I have a well-developed freighter network and many colonies to trade between, I'll have plenty of money for researching all the cool toys. That's when I start looking to invest in the techs and ships needed for a serious warfleet to start kicking my rivals' teeth in. What weapons I choose for my initial warfleet will vary from game to game depending on what race I'm playing and what I feel like using that game. Once I've got a couple warfleets put together, I'll start sweeping up a bunch of nice-to-have cheap techs I likely skipped earlier and also grab megafreighters, then I'll start working towards either stations or upgrades for my fleet if I need any.
It is nice to be able to go anywhere I want, but the (lack of) speed is agonizing. The lack of range for non-ER ships is also painful, 2 turns of travel exhausts all fuel. 
Need a tanker along to get a colonizer anywhere.
But I am not sure what to do when the other side just runs -- I don't have the speed to catch them, but am not sure what else to do. Just sit out the 4 minute clock? 
I recall a mention in the SG about the difference between retreat and backing off from combat, but I do not understand how to choose between the two. I do not want to retreat from the system, but can I break off the combat early without doing so?
And thanks to the players in the SG for getting me into this game. I am having fun, even if I have only the vaguest idea what I am doing so far. 
I need some colonizers out here quick. Although with my drive tech, "quick" is not really even remotely the right word....