Research summary:
Every turn you are between 50% and 150% you have a chance to complete, depending on several factors, most notably how much percent complete you are (close to 100 is good), but also modified by considerations such as tech boosting. You can't go over 150% and if you do you'll be refunded amount over 150% in cash. So this should tell you that the faster you research a tech, the fewer die rolls you'll have to complete the tech and more likely you will be to go over-budget.
As a result, there are a couple common research strategies:
1) Set the budget slider to what you can afford (i.e. what you don't need for planetary development and savings for ship construction/morale) and leave it there. Not necessarily the most efficient approach, but the simplest.
2) Balls-to-the-wall. Appropriate for cheap techs you can research in a turn or two. Paying 150% dollar cost on something cheap is still cheap, and not wasting extra turns in over-budget can be a valuable thing in its own right.
3) Sprint-and-drift. This is kinda the opposite of 2 in that you're trying to save money at the expense of time. Push research to the max for the first bit of the tech until you get to 50% (make sure you have enough savings to be able to afford a few turns of full research.) Once you're at 50-60% or so, dial research spending way back (25% or less of your budget) and take it easy, waiting for the tech to complete -- at an increased chance of being under-budget, since you're taking extra turns and getting extra die rolls, and building up a nice nest egg for your next sprint phase while you're at it. Works best on more expensive techs that take at least a few turns to finish.
Note that nothing is guaranteed no matter which way you do it, except that it will never take more than 150%. In every other case, you are playing the odds and have to expect that things will not go your way sometimes. I find I tend to start games using sprint-and-drift a lot, but as the game proceeds, my freighter networks come online, and my economy matures, I start using sprint-and-drift much less and the first two options more.
Re: TARs:
Check out the link I provided to the Forum Archive:
http://sots.rorschach.net/Strategy_And_Tactics_Forum_Archive
There are lots of good links to TARs in there, including several of mine. These are solo efforts but many of them provide a lot of great details on gameplay. One note -- the Kerberos forums moved a few months ago so for some of the older TARs, many of their image links may be broken. You can also find the reports of the few SGs that have been tried there in the Collected TAR Summary link supplied on the forum archive page, also copied here:
http://www.kerberos-productions.com/forums/viewtopic.php?p=248096#p248096