We are upgrading from Sitecore 7.2 to 8.2. In 7.2, we have many sublayouts (.ascx controls). What's the best practice on upgrading those? Should we just migrate the site with the sublayouts or do we need to convert these in MVC renderings?
For upgrading I recommed you to use Sitecore Upgrade Tool.
The release supports migration of any version of Sitecore 6.6 or Sitecore 7.2 to the Sitecore Experience Platform 8.2 Update-1 and migration of Web Forms For Marketers module 2.4 to Web Forms For Marketers 8.2 Update-1.
You don't have to rewrite sublayout, site it will work but is recommended to switch entire site from Asp .Net Webforms to Asp. Net Mvc
As mentioned here already, use the Sitecore Express Migration tool: https://dev.sitecore.net/Downloads/Express_Migration_Tool/20/Express_Migration_Tool_20_Initial_Release.aspx
Note that this will migrate the data to a new clean instance (always use clean instances when upgrading).
Onces your databases are migrated to the new version, you can update the code. You do not need to move to mvc at this point if you don't want to. It might be recommended to do so at a certain point, but you are not required to do this now.
You are required to update any references in your code to Sitecore (use Sitecore Nuget, this will make your life much easier).
You should check the Sitecore compatibility table for any further necessary updates (https://kb.sitecore.net/articles/087164) although I think you should be fine there.
When you are using a DI-framework, remember that Sitecore changed some things on that in 8.2 - you will need to decide to adapt to the built-in (MS) framework or add some code to use your existing. Also make sure to check your global.asax code (Global.asax Application_Start not hit after upgrade to Sitecore 8.2).
After your code has been adapted, publish it to the new migrated instance and you should be good to go.
Sitecore 8.2 still supports both MVC and Webforms. However, a page should be either completely webform or completely MVC. This should not be a blocker in your case as you will be upgrading existing application on Sitecore 8 webforms