Both Apache and LGPL are compatible in the way you are using them: as different components. It would be more complex if you were trying to combine in one component code from several licenses under a single one (although the licenses you use above would allow under some conditions to relicense the code to certain licenses).
What you should do¹ is to include with your program a list of components you use with their licenses and their source code (it can be a download link to your website). If you changed the component, publish your modification under the same license.
Given the above licenses of the plugins used, you may publish your program under any license you choose (all of those mentioned are fine: Apache, proprietary, GPL, etc.) Note that for GPL you should include an exception for the components, so there's no need to relicense them for GPL compatibility.
Mention the components and their licensing where you place your main program license.²
¹ This is actually stricter than what you are required by some of the licenses, but it's good citizenship (and also keeps you on the safe side).
² It may range from mentioning the components license files on a COPYRIGHT file to including the full text of the licenses in a window which is showing your EULA.