Why bother about color profiles?
First of all you need to accept that different printers follow different standards. The same CMYK numbers will look differently when printed according to different standards. It's not possible to make a PDF which will be perfect under all circumstances. Unless I absolutely have to, I wouldn't export a PDF for print before knowing where the document will be printed, on which kind of paper and which ICC profile the print house recommends for that paper.
To use the wrong profile can affect the colors on the final print, but even if there is little difference between the profile you choose and the recommended one, there is also a responsibility issue. If you receive a print where you think the colors are a little bit off and the print house discovers that you didn't use the recommended profile, they might park the complaint right there. Always best to keep your path clean.
Setting up your document
Setting up Working Spaces in the Color Settings affects new documents, but you can always change the settings for an existing document later by using Edit > Assign Profiles. You can also choose a different profile when exporting a PDF. So you are not confined by what the settings where when you created your document.
The main reason for caring about which profile to use for your InDesign document from the beginning is that it affects the preview.
In a print document, when you turn on View > Overprint Preview the graphics and images are displayed as they would look if they were printed according to the Document CMYK.
RGB swatches
Although all swatches in a print document will be CMYK by default, it's also possible to make RGB swatches. They are assumed to have the RGB profile chosen as Document RGB and with Overprint Preview turned on they are displayed as if they were converted from that to the CMYK profile chosen as Document CMYK.
RGB images with an embedded profile
If you are a little in doubt about color profiles and don't know exactly what you are doing and why, I would always recommend to only place RGB images with an embedded color profile. With Overprint Preview turned on they are displayed as if they were converted from their embedded RGB profile to the CMYK profile chosen as Document CMYK.
For example an RGB image looking like this:

Will look like this with Document CMYK set to Coated FOGRA39:

But with Document CMYK set to PSO Uncoated, it will look more faded because the gamut is smaller:

Untagged RGB images
RGB images without an embedded profile are a common cause of a shift in colors from screen to print. They are displayed in Adobe's applications as if they had the profile chosen as Working RGB in Photoshop or Document RGB in InDesign. So if your Photoshop for example has Adobe RGB as Working RGB and your InDesign document has sRGB as Document RGB, the untagged images will be displayed differently in those two applications.
Here is how an untagged image (which is is in reality an sRGB image) is displayed when InDesign assumes sRGB:

And here is how it looks if InDesign assumes Adobe RGB:

Untagged RGB images should be opened in Photoshop and have a profile assigned. 99% of the time it's sRGB, but if it doesn't look right you can try Adobe RGB. It's a guess.
CMYK swatches
You probably make your swatches as CMYK swatches like most of us do. This is fine, but be aware that a CMYK color is not an absolute color. You are "hard coding" the percentages and the color will appear differently when printed according to different standards.
A mistake I often experience is people creating a document without thinking about the CMYK profile and thereby unconsciously choosing U.S. Web Coated (SWOP) v2 which is standard in Adobe's applications. Then they carefully fine-tune their CMYK swatches until they look as they want on screen. When they export a PDF they suddenly remember that they need to choose the correct color profile. They convert with Preserve Numbers to keep the black swatch at 100% black and thereby assign another color profile to the document. All the CMYK values are unchanged, but the intent of the document changes and when they see the document in Acrobat they notice that the colors have shifted.
The colors they see when designing in U.S. Web Coated (SWOP) v2 might look like this:

But after exporting and assigning Uncoated FOGRA29 the colors look different:

CMYK images with an embedded profile
Depending on how your Color Management Policies is set up, CMYK images with an embedded profile will either be Preserved, Ignored or Converted. You can see a detailed description of each in the Color Settings dialogue. I wouldn't recommend for you to place CMYK images unless you know what you are doing and why.
Untagged CMYK images
Has the same problem as untagged RGB images. You don't know which profile it was converted to. InDesign just displays the image as if it was printed according to Document CMYK. If that profile isn't the same as the image was originally converted to, there will be a shift in colors. Avoid this issue.
Common standards
If you are forced to guess which profile to use, here is a list of commonly used profiles.
Europe
Coated paper
- Coated FOGRA39
- ISO Coated v2
- ISO Coated v2 300%
- etc.
Uncoated paper
- Uncoated FOGRA29
- ISO Uncoated
- PSO Uncoated
- etc.
North America
(Americans, help me out here!)
A way to make a general PDF?
I'm not sure I would recommend it, but if you really want to make documents which could be used on any printer, you could make a mix of RGB and CMYK. Keep the black text as 100% CMYK black and all neutral objects and images in percentages of black. All other objects and images could then be in RGB. This would enable a print house to convert your PDFs to any profile they wish without too much hassle.