Personally, I’d actually go ahead and just jump into Cycles. Probably a lot of people are about to scream at me for saying this, but here’s my reasoning:
I think, as a learning renderer, it isn’t bad. In a lot of ways, it’s simpler to learn than BI (the reasons for that will become clear after you’ve used Cycles and BI for a while…)
In BI, you can do some amazing things, and it renders animation pretty quickly. However, to do things very well, you really have to know what you’re doing. Also, BI can produce weird artifacts (from poorly setup lighting, among other causes…) that can be extremely tricky to debug. And that means, although almost everything in a vid looks great, you’ll have to go back and re-render that section after you’ve figured the problem. In Cycles, that almost never happens. And, since it’s very quick and easy to set up, you don’t get the hours of guesswork you sometimes run into with BI, make a little tweak to a texture, F12 render, repeat.
The problem with Cycles right now is that rendering animation does take longer than BI, even if you have a decent graphic card. So, instead, you learn some clever techniques to knock down render times some. No matter what, you’ll still get scenes that are more realistic than BI. And, as hardware gets faster, so will Cycles.
There are things BI can do that Cycles can’t, yet. However, you can do those things in BI, then composit them as special effects into a Cycles render. Just like makin’ a real movie.
At any rate, there are positives and negatives to both, and they are both free, and that’s awesome. I’d say learn both and get very good at both. But, as a beginner, that’s a scary proposition. So, I’d say start with Cycles. Because of the realtime preview window, you’ll get a very good feel for how your tweeks will affect your scene, and that’s hard to do with BI sometimes (sometimes you won’t even know how something will look in BI until you render an animation, then you suddenly see all kinds of grisly problems…)
Then, once you’re good at Cycles, you can learn to get really good at BI, which has plenty of strange pet knobs and kinks.
Either way, have fun, AND DON’T GIVE UP.