Other very good cubes apart from the Shengshou Aurora (which I agree is a very good cube) are: YJ/Moyu Guanlong, YJ Sulong, YJ Chilong/Yulong, all of which can be found for 4 bucks or even less. Of course there are other even greater cubes (but more expensive, around 7 to 18 bucks) like Moyu Weilong, Aolong and Hualong, Gans 357 and 356, Cong's Design Yueying and Meiying, Fhangshi Shuanren & Guangying... You'll have a hard time choosing just one
From all the 1t ones the only one you can find stickerless is the YJ Yulong but to be honest I started with a stickerless cube and got bored of the colours pretty soon. If you use a stickered one you can always choose the colours. That's up to you, of course.
Regarding pillowed cubes I wouldn't recommend a pillowed 3x3 for speedcubing. It is more difficult to grab and fingertrick with.
Most commonly used methods are CFOP, Roux, ZZ and Petrus. I have tried the 1st 3 but I have only become somewhat fast on CFOP. Anyway this is just because I started with CFOP but I also like Roux and ZZ a lot. You can read a guide to choosing your own speedcubing method in the How-To, Guides section of this forum, more specifically here:
Beginner's Guide to Choosing a Speedsolving Method