That's like asking 'what is the best pencil to draw a picture with?'
There are many web-design applications, and which one you use to design a site will depend on a number of factors - one of which will be your budget. Other influencing factors might be the type of site involved, or your personal preferences and level of design experience.
The first thing to say is that you should forget about designing and developing web sites professionally using a tablet. Technically it can be done, but you would not enjoy the experience. I've designed and developed sites using a laptop, but the job is much better done with a desktop machine and a decent sized monitor.
Speaking personally I use Microsoft Expression, Adobe Creative suite 6, and sometimes Serif WebPlus X6.
If you're a complete beginner you should understand that you're in for a pretty tough learning process before you can offer yourself to clients as a professional designer. You'll need a degree of design ability, plus technical knowledge of the various aspects of site design, including e-commerce integration. The way to learn is to get some initial software - I recommend WebPlus X6 to start with - and become familiar with it. Register a domain name for yourself, sign up for a basic hosting package with a decent web host, mock up a site, and publish it to your server space. Create sub-domains,and publish other test sites to them. In this way you'll start to get a feel for the problems and their solutions.
You can teach yourself, but it takes a while - how long will depend on your personal abilities, and your determination, it's a hard slog to start with because you'll hit problems one after another, and that's all before you even begin to look for customers.
Feel free to come back to this thread with questions as they arise.
Good luck for the future.