Well, by far and away your biggest question should be: is my game going to be commercial? If so, then you will have to obtain a Source engine license, which is going to be (in most cases) substantially more costly than other engines, especially options like Unity. From the jist of your post I assume you aren't going to be commercial, though.
If your game is not going to be commercial, you can use the Source engine for free, but then you will have limited access to the engine and be at the mercy of the SDK tools. Valve has not done a great job (I am putting this lightly) at maintaining the SDK lately and the tools remain in a near-broken state.
Personally, speaking as someone who has worked on multiple Source SDK mods since 2005, I would stay as far away from source as possible. The tools are simply far too outdated and unkempt at this point. They have literally gotten worse as time has passed; for example the demo smoother tool (used to edit the camera movement in a demo to get good footage for movies such as trailers), has actually become harder to use from the Episode 1 SDK to the Orange Box SDK. It has more bugs and more crashes. The other tools can have the same said of them, OBSDK's Hammer (the level editing tool) now has multiple render bugs that did not exist in previous SDK versions, etc... it simply feels as if they do not care about their free tools anymore. It's a shame, as mods are a huge part of why Valve is what they are today. I do not know if their commercial tools fare the same (I would hope not!), but given what I have experienced with the free SDK there is no way I would ever consider purchasing/using the source engine for a commercial game.
As for other free engines, Ogre3D and Irrlicht are worth looking into as well. Also the Torque engine from Garage Games has just recently re-launched with a much lower price, $100 for their 3D engine, down from what used to be around $2000 iirc.