As a primer, since I'm lazy and don't actually beeline myself, there are a few points I've picked up.
Techs that are important to get to are 1. those that are considerably more expensive to research compared to their pre-requisites and surrounding techs; 2. techs that the AI prioritises, therefore are easy to trade for lots of other techs; 3. techs that give some kind of major benefit, especially if you get to them first. Here are some examples of the above...
Philosophy is quite expensive, the AI likes to trade for it and it gives you the option for the Pacifism civic (much much faster Great Person generation rate) as well as a religion if you get it first.
Code of Laws is relatively easy to get to, and is/was popular for players who would use the Oracle to get a free tech. It gives you a religion as well, and makes Courthouses available. This building is really important for keeping down costs of founding new cities if you're expanding, and can give you an edge if you get it before the AI.
Liberalism is a classic one, chiefly because if you are the first to get it, you get a free technology. You can make this something quite expensive, giving you two good techs to trade around. Also, there is a civic choice or two with this that is a big boost to the economy.
Construction is one the AI goes for like a rabid dog, so if you somehow get it first you can trade it around really happily. It gives you the Great Wall, which is invaluable as it prevents barbs from entering your land borders, freeing you up from having to look out for them. Also, any experience you get from battles on your own lands counts double for generating Great Generals. Finally, this tech allows you to build the first siege units - Catapults. Once these come along heavily defended AI cities are much more easily overcome, and they can save you lots of real highly promoted ground troops.
As for how to beeline, you can do that easily enough by identifying a tech you want to beeline to, then by going into the Science Advisor - either just as you've discovered a tech or whenever you like - and clicking on the tech. The tech tree automatically shows you which techs are the pre-requisites and will research them automatically for you until you choose to research something in particular. Great People are pretty good for beelining techs, since they can each 'lightbulb', i.e. instantly discover, certain techs for you. If you know which techs each type of Great Person can research and in which order (there will be a list somewhere here if you search for it), you can make sure that you lightbulb an expensive tech that gets you an advantage.
Hope these intro points help somewhat, and that someone who actually DOES beelining will be along soon.