Full disclosure everything I'm going to tell you here is learned from personal and sometimes frustrating experience. I don't consider myself an expert at all. I have yet to actually publish a game and have learned everything here the hard way. I've been working on this stuff for about a year and a half now. So if anyone else wants to jump in feel free.
For indie development first you need to decide what type of game do you want to make. Do you want to tell a story? Is story secondary? Will your idea be best served by 2D or 3D game play. Do you want to aim for realism or use a particular art style to enhance the atmosphere of your game. How long do you want people to play your game? Is this a short mobile filler like Flappy Bird or are you wanting to create an epic like Skyrim or Fallout. Do you want to include multiplayer? Will it be a separate mode? Will it be integral to the game?
Once you have at least some idea on these things, do some quick sketches. It can be full storyboards or just further developing the characters and story in a notebook. Understand your world before you try to bring it to life.
Once you've settled on the basics and have a good idea of the story (or simply mechanics evolution for something like Angry birds where the story is pasted on) then start deciding how you want to proceed on the programming and art side. Or sometimes you may do the process backwards too. You might say I have this really cool idea for a game mechanic and work backwards from there.
I personally like Unity3D but as far as graphics goes, the engine isn't really going to have much to do with it other than lighting ect. You can build some objects in Unity but it's usually easier to model them in something like Blender and import. What an engine really is, is a way of automating development a little bit. It has built in handlers for things like collision detection, audio triggers, and you only have to script specific behavior. In something like unity it makes it much easier to kind of visualize an idea without much investment of time. As far as switching engines goes, the objects will usually be compatible if they're saved in a non proprietary format, but you'll have to rewrite your code for the specific engine in a language it understands. Unity supports JS and C#. If you want to do web games you can do them entirely in JS and html5 with canvas. Gamemaker is another popular choice (which I have but haven't really used) as are gameguru (which I don't actually know what it's scripting language is but I suspect it itself is built on Unity and is basically drag and drop) , and app game kit(which uses a proprietary dialect of basic for its scripting). And of course you can write your own if you're a decent programmer. Java is easy to learn for this purpose. But if you just want to get in there Unity is great because you can use it for free to create commercial games as long as you're below a certain dollar threshold in revenue. And for audio editing I like Sonar but if you don't want to spend the money you can use audacity for your editing. Be warned though audacity is a pretty terrible DAW with poor midi support, middling vst support, and destructive effects editing. Steam I believe is having a sale on Sonar at the moment. So for my recommendation:
Decide what you want to make games for. If you want to develop for PC or Android your options are wide open and the financial barriers are relatively minimal. IOs is more expensive to get into, and the consoles are much more heavily controlled in terms of what they allow for things like XBLA.
Find an artist unless you're already skilled with a 3d modeling program. Or you can just go for it and learn to model or use prebuilt assets which are available in different places around the web. Make sure to search for royalty free assets.
If you are skilled with the art side you can find source code and just tweak it for a fee and develop your own art to go with it.
Unity is a powerful and well supported engine that seems to really be aimed at developing independent talent and has a great community. I really like using it.
Get a decent DAW and a small control interface like an Oxygen25. Sonar or Reaper are both good for this purpose. And a proper control interface will make your life so much easier.
And if you want to not code your own AI(assuming you mean true pseudo AI and not just telling enemies to move in a certain direction ect), look into Gameguru because you'll need to be able to write your own AI to use something like Unity. There are plenty of tutorials out there though. The big thing I'll say is don't ever think this will be easy or fast. You're going to have to put in time to learn the tools and languages and learn them well if you want to produce anything of quality.
Good Luck
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