Can you select the 'faster' clips, slow them down 20% and then save at the faster frame rate?

Different editing programs handle this differently.  I work in video production and run into this quite a bit when people bring us stuff that they shot to combine with something that a friend of their shot.  In my edit program (Adobe Premiere Pro CC 2014) most of the time you can just drop both clips into a single timeline and export it at your desired frame rate and it will do a decent job of converting which ever clip needs to be converted.  Sometimes to get better results we need to convert first.  The problem lies in the fact that neither frame rate translates well into the other.  To get 24 FPS to 29.97 FPS there has to be frames added at a strange ratio, and to get 29.97 FPS to 24 FPS you have to take frames away at a odd ratio.  You can run into more problems if the 29.97 footage is interlaced video, since the 24 FPS video is going to be progressive.  If the 29.97 footage is progressive you will have a easier time getting them to work well together.  Just make sure when you export the video that it is progressive as well.  

I don't know if that helps, or if it made it more confusing.  

Phil

Phil has done a pretty good job explaining the situation.

The two primary options are to adjust the footage frame rate as you import the footage or indicate what you want the uniform frame rate to be once you export the final project.

There is another possible option where you could possibly use timewarp to slow down the 30fps shot to match the 24fps.   I haven't done that, but many use timewarp for slow motion shots (like on a gopro) that is shot at a higher framerate (60-120fps).  You can pretty much adjust the framerate "flow" if needed.  Of course, you can also adjust playback speed right in a program like CS6 PP or CC.

The issues that might come up would be audio matching the subject, but you stated that you wouldn't have shots that would have people talking.  Another issue, that you should see on the footage is the lighting value differences when comparing the two shots--that is, unless other adjustments were made (ISO, aperture...) to ensure continuity.  

Have fun.  Isn't editing great?!?

That really is the best idea that will yield the best results. 24p is pretty popular, but I just do not like shooting in it.  It is not as forgiving either, especially for newer shooters.  You have to pay a lot more attention to pan speeds and moving subjects.   I personally shoot 99% of everything I do in 1920x1080 60p.  It converts well to 30p formats for putting stuff online, and it also converts well to 60i, either for 720x480 29.97 for standard DVD, or 1920x1080 60i for Blu Ray.  If you are shooting sports and want to keep the HD video at 60 FPS, you can also easily scale down to 1280x720 60p for Blu Ray.  The only downside to 60p is that you need faster shutter speeds which means more light.  

Video is such a wonderful and complicated world.

If you have to have 2 cameras it is best to get two of the same camera.  They all handle things a little different.  Even in two different cameras that shoot 30p, they will handle colors, light, white balace, etc differently.  You will pull your damn hair out trying to color match them in post.  Color correcting on consumer lever footage is frustrating as it is, even more so when you are trying to match two together.   If you can get away with it, and have to time during the shoot, you can just use the same camera for multiple takes, from different angles.  It can cause a little more trouble is organizing, when you start editing, but once you have everything sorted out it would go just as any multicamera shoot.  Organizing your footage, graphics, titles, etc is also a huge part of editing, and often overlooked by newer editors.  For small projects it is not as big of a deal, but as the projects start growing it can become time consuming just trying to find stuff.

Good luck, and have fun with it!

Phil