If you want to use Visual Studio, you need Visual Studio 2015 and CTP6.
Good news is, you can have VS2015 installed side by side with 2012 or 2013 with no problems. (really!) And if you are not yet familiarized with the command line tools, I do highly recommend to install vs2015.
For migrations, there's some documentation in the workings on the Docs repo.
check this out : https://github.com/aspnet/Docs/blob/master/docs/migrating/migratingfrommvc5/migratingfrommvc5.rst
this is just one, there are a few more doc pages on that repo that might help you to get started and see which changes should be made and how to apply one by one.
Unfortunately the documentation is not finished and there's not much about it, so be prepared to have patience because you will be migrating and learning a new stack in the process.
Microsoft team has been very active and helpful in all channels (twitter, SO, github, etc) so, you can at least get help if you find a block.