I am working on a migration project(6.2 to 6.5). My all static templates are made with heavy JSP implementaion. Now to proceed on migrating static template to editable template, i am wondering if we can use same JSP scripts and try to include templated container snippet from here (/libs/wcm/foundation/components/basicpage/v1/basicpage/basicpage.html). or creating the whole new template in HTL is best way to approach it.
AEM migration projects should be seen and planned on multiple levels. Many customers tend to split the migration into multiple phases for each of them, e. g.:
Migrating the existing platform (6.2 to 6.5 in your case) - basically updating the dependecies (primarily: the AEM uber jar) and getting your existing application and website running on the new product version.
Source code modernization - projects that have been developed for older versions of AEM usually have quite some "legacy" code that does not reflect the latest development best practices and recommended patterns. So refactoring your existing code base to modernize it should be on your list.
Adapting new features - newer versions of AEM come with additional features that you may want to leverage. One that seems to be a priority on your list is Editable Templates. As your question is specifically about this, I'll give some recommendations below:
When existing projects want to leverage Editable Templates it is important to be aware that a "simple" 1:1 migration usually isn't the best approach. Editable Templates have many advantages that bring most benefit if you design your template around these capabilities. In addition to that my personal recommendation is to evaluate your template requirements to see where you want/need Editable Templates and if static templates are still a good fit for others. While it's totally possible (and probably recommendable for green field projects) to run your platform/website completely with editable templates, they also come with certain complexity. Therefore, most existing projects moving to editable templates go with a mix of both approaches.
So the bottom line is: when migrating to a newer AEM version and modernizing your project, it is not mandatory to move all your templates to be editable. Evaluate your setup and requirements and decide for which ones this makes sense and for which ones it does not.
When it comes the actual implementation, I totally agree with @Ravi_Pampana: don't just move your JSPs but migrate to HTL. This is more important then actually moving all templates to be editable. You may want to have a look at AEMs Modernization Tools  to see if they can help you with your overall upgrade and migration.