Doom 3 comes with all the necessary editors, besides 3d modeling and photoshop

The opensource engines with free content are nice because you can distribute your mod as a complete game. That way you don't have to depend on your audience owning, say Half Life 2, to be able to play your mod.
free content total conversions examples:
Freedoom --> er ... Doom engine? :o)
Nexuiz --> Darkplaces/ idtech 1
OpenQuartz --> idtech 1
Tremulous --> idtech 3
Open Arena --> idtech 3
Inside3D is great site for Quake engine modding.

One of the great things with Unreal is the extensive amount of videos available to help beginners learn how to use the tools. If you buy collector editions of UT2k4 or UT3, which are extremely cheap now, they come with an extra disc full of bonus content on how to start modding.
Granted I did not mod for long (was mostly just curious how it all worked), the Unreal tools seemed easy to grasp and use compared to Source, and I was able to do the basics in no time.

Yeah that's true. There are over 20 hours of tutorials supplied with the limited edition of UT3 and like you say, it's dirt cheap now.

This pretty much rules you out from doing anything other than play around with various model or level editors. You need strong coding knowledge to go one step further and actually create a game or application.

Not necessarily, depending on what scripting language the game uses it doesn't have to be difficult to learn, especially if some coding experience is already present.
Knowing PHP is at least a much better start than no coding knowledge at all.

What are you talking about? If he's going to buy a game and use the games available editing tools to make mods / maps, then why is he asking about 3D engines?
Obviously, if you want to do that, buy UT3 and have fun with the level editor.

I figured he was asking for a good tool to create his own game out of, and knowing C isn't (always) a requirement if he don't want to modify the engine to do more than it already does.
Sure, I'm not working with an advanced 3D engine, but I'm very much making my own game using the Infinity Engine, not a mod requiring Baldur's Gate 2 to be installed (even if I am building from that base and using it as a template). The required coding is LUA for all scripts the game is using, and Python because that's what GemRB is using to interpret the different games. Neither of those are that hard to pick up for someone already regularly coding in just about any language (my expertise lies in PHP and a fair bit of Javascript, I've done a tiny bit of LUA for a World of Warcraft add-on, other than that, I can read most languages but not necessarily write them).
While looking for translation files to expand my thread about multilingual games I found out that just about everything in MDK2 is made in LUA as well.
I figure that more often than not the "game" is really written in some high-level scripting language that reads all game data and sends it through to the graphics, physics, and sound engines, making it unnecessary to learn "real" programming languages, as you can make use of that scripting language and the binaries the game runs through (of which there can exist open source versions - like the id engines or GemRB), if you don't make use of the original data files it's not a mod, it's very much a game in its own right.
Sorry, I'm ranting, I should sleep.

Just for the record, I'm not looking to create a fully fledged game; just a tech demo of sorts. Just to see if this idea that has been naggging me for a long time is possible in any way. If it proves possible then I might seriously consider trying to find modding team/indie developer type persons who are interested in furthering the concept to a near-professional level.
But it's far more likely that nothing will ever come of this at all =)

Considered the Cube engine(s)?
Also, there's always Torque if you're serious and actually planning a release of some non-commercial variety.

Hey, you never know. Besides, worst case scenario you have an unfinished idea that someone is conceiving at the moment and will make eventually.

I don't know about this. Steam has been quite bitchy when it comes to letting users access the games without Steam, and from what I understand, to use the Doom 3 map editor, you need to actually boot up the game with a shortcut that access the .exe with certain commands so that the map editor starts up fine.
But if you really want to have a hand at modding, or at least taking beginner steps with 3d modeling and texturing, I suggest getting a retail copy of Doom 3 cheaply. I can help you along the way too.

Torque's great. With some decent skills, you can actually produce something good out of the engine. Plus, the developers of Torque are constantly updating the engine, so it doesn't fall too far behind the latest tech. Well ok comparatively it's still not as robust as id Tech 4, but you get what you pay for.

The Steam version of Doom 3 does indeed allow access to DoomEdit. At least that's a start =)

Nice. Have you found the list of tutorials over at doom3world yet? There are several basic mapping tutorials to start you off.
I really like how easy it is to mod Doom 3. Just tweak a def file to get a "different" weapon, or tweak the Hell Knight's AI .script to change the behaviour of Hell Knights. It's a shame that so many people were scared off by unfounded rumours, as proven by several powerhouse mods out there, such as The Dark Mod and Fragging Free.