Well, what do you NOT want people to do with it?
If you use GPL, then the software authors are obligated to make available the sources of their application to anyone they distribute the application too.
With LGPL, they're only obligate to distribute changes to your system. That is, if they changed any of your runtime to support their application, then those changes would have to be made available to those they distribute the application to, but the application sources themselves would not be under the same guise.
There's also the AGPL, which is essentially GPL for services that are not distributed in the conventional way. Many folks use GPL software on computer servers, but are under no obligation to make the source code available, since they never release (and thus distribute) the software. AGPL handles that use case to promote source code release of these kinds of systems.
There are other "forced source" licenses (MPL, CDDL, etc.), but they're tied to the actual licensed code and changes to it (like LGPL).
If you want something more "I don't care what you do with it", then the BSD, MIT, and Apache licenses are available. These are about as close to "public domain" as you can get with a license.
The "I don't care" licenses are easily embedded in other applications and impose no burden on them whatsoever outside of, perhaps, an acknowledgement that they're being used.
So, anyway, it comes down to what you want from others with respect to your software. Expand on that, and I can give a more nuanced response.
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