If you want a really good, cheap cube get the YJ Sulong off thecubicle.us or some other site. It's only $6 and is damn fine for a beginner. Or if you wanna get something different for more some good options are:
>Dayan Guhong: absolutely great to learn how to tension and lube cubes, plus you really don't need much more than CRC to make them really fast. The only downside is if you're tensions aren't fairly tight, it pops sometimes. But it's great for learning accurate turning, as it is forgiving and doesn't pop very much in my experience
>ShengShou Aurora: the track system gives it a very buttery feel, and it has good corner cutting both forward and reverse, plus it's cheap. But the turning style is kinda different, and it isn't everyone's cup of tea, but for only $9 it's a solid cube to try.
>Dayan Zhanchi: very quick if you set it up right. Personally, I wouldn't recommend something like this till you can sub-30 on a slower cube, but it is an option if you take to the statement "go big or go home"
>Moyu HuanYing: this cube can be quick, but I could see it being good for someone coming from something fairly quick like a V-cube.
>Dayan Lunghui and LingYun: both of these are very swaggy cubes. they could be a competent sub for the Guhong if you're feeling like taking the road less traveled when it comes to mains, they've all got that solid Dayan-type feel to them.
Having started with something fairly quick, you can pretty much go to anything you feel, but I'd recommend jumping up to something of intermediate speed and just practicing technique to get faster. If you can get sub-20 on a slow cube, your times will plummet like crazy when you get a fast cube. Personally, I'd recommend a Guhong v1 or v2 the most, I love those cubes and I prefer them to my CRC-d Zhanchi.