There are no such things as Symbian Series 40 or Series 60.
Nokia Series 40 is based on Nokia's proprietary operating system. For third party application development, you can use Java ME and MIDP, Flash Lite or widgets (i.e. XHTML+CSS+Javascript).
Nokia S60 is based on Symbian OS. In addition to what you can use on Series 40 for third party application developement, there are the options of using C/C++, Python for S60, Perl, Ruby etc. (though the last two do not yet have significant community traction).
In the future, S60 will be merged to Symbian Foundation platform releases. Current S60 5th Edition is likely to be the last S60 release from Nokia; the next platform release will be Symbian^2 from Symbian Foundation, corresponding to S60 5th Edition FP1 in the old S60 versioning scheme.
For both, you can find the tools and SDKs from Forum Nokia, alongside other developer resources.
Web services (sending data over HTTP, parsing results) should as such be usable on all of these platforms and technologies, although I don't have experince with all of the combinations.
And last thing: could you clarify what you mean by third party application integration?
Edit after OP's comment: Yes, in general third party integration is possible on all technologies to some extent. For more specific answers, you should frame more specific questions :)