I'd say pick any engine that you've already seen produce a game type similar to the game you want to make and check the forums for that specific engine.
Unless of course you want to write your own engine, in that case grab as many open source engines as you can and start dissecting their source code. The id Tech engines are great for this because they're very, very widely documented.
I program games for a living, and I made small games on my own for a long time before that.
For someone starting out, I would definitely recommend using Unity. It's a good engine, it's free, it works on just about every platform out there, and you can program in C# which is generally a very friendly and nice language to work in. They also have lots of tutorials, training videos, documentation, and a very active community of developers. Finding a good community can be really helpful when you're starting out, since they can guide you onto the right path and walk you through common problems.
As far as general advice goes, I would say try not to get overwhelmed or discouraged, especially if you start on a project that doesn't end up working out. Games are amazingly complicated, and it takes a long time to build up all of the various bits of knowledge required to make everything work together. So if you come across road blocks don't beat yourself up, just learn all you can and maybe narrow your scope so that your games turns into something that you can finish and be proud of.
@Dougy_No_1: If you're just starting out, here are some pointers:
Start small. I would start by making clones of classic games like Tic Tac Toe, or a card game. If you try to be ambitious from the start, you'll only frustrate yourself. You have to learn how games work before you can begin doing your own thing.
Go to game jams. Check out stuff like Ludum Dare or Global Game Jam.
You have to know some math and/or physics. You don't have to be a whiz or anything, but games involve math or physics to some degree. Depends on the game.
There are many resources you can use for free images and sounds. I can't make sounds, so I use freesound.org whenever I need something.
I would create design documents of every game you want to make. It doesn't have to be for a game you want to make right now, it could be something for the future. The point is that you write them down so that you can refer to them at any time. They don't have to be complete, and you shouldn't expect them to be complete. I currently have 25 design documents for games that I want to make or have made a prototype for, and out of those, I have 3 that are high priority. If you like, I can show you one of my design docs to get an idea of how you can write yours.
Games always take longer to complete than you think!