The 11z and the HP you linked to are basically the same. They have different CPU speeds, hard drive sizes and such, but they're both built on the same Intel CULV platform. It's like two different cars, which are the same underneath. They have different stying, engines and options, but they're basically the same.
So, you'll have to judge which options/price are important to you.
When spending alot, I'd prefer a multi-core CPU, though. The dual-core option for that platform is usually called a Pentium Dual Core, should be an option on both models, but it might be overpriced.
The 1012 uses a "lesser" platform, slow CPU, very limited graphics performance, etc. On the plus side, it's cheaper and smaller than the others, and still offers enough performance for basic use.
If you need more clarification, feel free to ask followup questions.