Handling Frame Rate for Movies with Slow Motion
The reason we try to shoot at our target frame rate is because if we need to adjust the frame rate, the computer has to invent new frames to go in between our existing frames.  This can result in artifacts in the image and generally reduces the quality.

You are correct that 24fps is the standard for theater and also correct that you need to shoot a faster frame rate for slow motion.  In general, the best way to deal with a shot like the one you are talking about is to shoot at a multiple of the frame rate you want for normal action.  If you shoot at 48 or 72 fps, then the computer doesn't have to invent any new frames to reduce to 24fps, it can just drop every other or two out of every 3 frames.

This is why you see a lot of 240hz TVs these days.  There isn't actually any content that works at that refresh rate, but 240hz TVs can properly display either 24 frames per second, 30 frames per second or 60 frames per second since they all evenly divide.  The same thing applies when shooting video.

Unfortunately, most consumer cameras, and even some professional ones, don't support multiples of 24 for their high frame rate options.  There are some cameras, particularly some of those made by Lumix, that support 240 fps video, but the quality level is pretty highly reduced when shooting at that rate.  120 fps would also work.

Alternately, you could give up on the 24fps and shoot 30fps instead.  30fps isn't the end of the world and there are existing pulldown options for converting to 24fps.  30fps was (roughly) the NTSC video standard and still works just fine if your main target will be playback on computer screens or TVs that support multiples of 30fps playback.  This is a nice even multiple of 60fps.

One final option to consider is interpolated slow motion.  Since many cameras reduce the video quality available at high FPS, the best result may be to shoot at a lower frame rate and have the slow motion interpolated from the frames you capture.  The results for this technique also vary greatly based on how good your software is, but there are several very good tools out there.  Twixtor is generally the best, but it is also expensive.  After Effects also includes TimeWarp which does a decent job.  This may be the best option for maintaining both maximum quality and minimal cost unless you have a pretty significant budget to work with or have other reasons to need to limit yourself to 720p or lower quality.

The ideal is to shoot the frame rate you need for the shot. Do your homework, actually think through the flow of your film.  Shoot the slow motion shots by themselves and use the correct frame rate for each shot.  If you need to do slow motion mid-shot for some inexplicable reason, decide based on what will cause the least harm.  If most of the shot is slow motion, go with the higher frame rate and interpolate to 24, if most of the shot is normal speed, shoot 24 and interpolate for the slow motion.  This should only be a last resort though! Shoot distinct shots at distinct speeds and use editing to blend them together properly.  That's the entire point of editing.