I don't have any real advice for which engine to use, but as far as your game concept, I would check out

Take a look at "how to make games without programming" and "more ways to make games without programming".

As an artist with minimal or no programming knowledge -- and from my understanding a fairly minimal desire to learn these things if you're able to avoid it -- you would probably be well suited to a package such as Construct 2 or Game Maker, both of which are definitely capable of producing a card game if you take the time to use them properly. There are other similar packages you might also wish to investigate listed in the above articles.

You could also take a look at BYOND, but it does require more programming -- albeit in a relatively simple language -- to get anything done.

I'll also just take a moment to quickly point out that you may possibly be heading for legal problems -- if you use the copyright or trademarked material from existing games -- such as character designs, names, etc. -- you're risking being sent a cease & desist notice or even being taken to court, even if your project is free/not-for-profit. It's fine to make a similar game, but unless you're willing to take the risk I would strongly recommend creating your own characters rather than re-using those that already exist.

Hope that helps!

It might also help to know what platforms you are looking to make this "game" run on when it's completed. For consoles you start getting very limited on your engine selections, and either requires lots of money or lots of coding knowledge to use (At least anything decent.). PC's have the widest range and there can be lots of various options to use, I'd agree with jbadams about trying Game Maker or Construct 2. If you want to target mobiles or web browsers (which might be the same thing) you are probably going to start running into even less game designer kits that don't require programming.

Just as a bit of personal commenting here, I would personally suggest doing this as a web based game. This will require that you partner up with a programmer or contract out the development of a game system but will give you a very large reach of potential players (if done right you can port it directly to mobile devices). Good web programmers can easily create web page editors for you to use to create cards and rule sets, incorporate a player / members system and there you go. You can sell card packs, advertising space or just charge a monthly subscription. Lots of good stuff you can do with card games on the web, new HTML 5 and jQuery animation features are pretty smooth and could handle quite a bit to make it all look nice. You can develop a simple and quick rule system that allows you to build rule sets from a point and click interface. Offer player tournaments and leader boards and such.

Anyway, to get back on subject a bit. You probably want to ask yourself and decide for sure what platforms and devices the end product should run on. Remember each has it's own limitations and trying to develop for "everything" is just a fools move. It takes to long and gets very expensive no matter how you approach it. You will always need to purchase or pay royalties for expensive "commercial" grade libraries and licenses, you will need more programmers or more expensive programmers, more distribution licenses and so on. Once you know where and how you want to distribute your game I would HIGHLY recommend that you partner with a coder and go from there. I personally am not aware of any game projects that have ever succeeded without at least one programmer.

[quote name='Dan Mayor' timestamp='1356916209' post='5015921']
I would personally suggest doing this as a web based game. This will require that you partner up with a programmer or contract out the development
[/quote]

I'd probably second this recommendation, but just wanted to quickly note that this still doesn't necessarily require a programmer: Construct 2 exports to HTML5, Game Maker has a version which can, and there are a number of other similar packages that feature HTML5 export. It's actually easier than ever to target the web-browser, and both performance and feature sets are being improved by leaps and bounds.