What is best to use?
Where should I start?
From the very beginning usually, but it depends on your background we don't know.
How can I achieve all this, is there any jQuery plugin for it?
If you use PHP, it's PHP + database + jQuery. Plug-ins? Many, but you will have to look them through.
] + many from third parties.
Can I do this thing with Jquery and AJAX?
Yes, this is what you would really need, + PHP +database. AJAX is just a part of jQuery library, for that matter:
When user has done all the changes how can I submit changed look and feel of the art into database, so that user can add it to cart to order further?
Despite the question mark, this is not a question even by syntax. Yes, you will be able to achieve all that; this is just one aspect of what you need.
Please guide me from where should I start or learn and what are the best available platforms?
Not a question, again, despite the question mark. (Many inquirers do exactly opposite, some questions without question marks.
Unfortunately, we don't have resourced for detailed individual guides, tutoring or something like that. Better ask more specific questions as you go. If you need a guide throughout all stages of the project, perhaps you are not ready to take such job.
And what else? Yes, better don't try to work with real money with your own code — too easy to loose them if you are not careful or simply have less-then-perfect experience in highly reliable code. You should look for some available reputed open-source code for it.