I hope you have seen and are at least nominally following the Migration Tutorial.
minimal
This will have just core OH without anything else installed, including PaperUI.
Over time the UIs have grown more and more capable. But there is nothing that requires the UIs. The migration tutorial tries to present both the UI approach and text file based approach. Coming from OH 1 you will probably desire to stick to more text based and relegate PaperUI et al to experimentation and play until you learn a bit more how they work.
Follow the text based configurations sections of the Migration Tutorial. It walks you through getting your current OH 1.x working on OH 2.x core without using any OH 2 specific concepts or bindings (i.e. all text based configs, all 1.x version bindings, no changes to .items, minimal changes to .rules, no changes to persistence and sitemap). Then you can choose to migrate to the 2.x version of bindings you are using (or never migrate) at your leisure.
You can use all text based configs. You might need to use the karaf console for some debugging but that is unlikely.
Yes, you will need Eclipse SmartHome Designer 0.8 (look at the installation section of the Docs for links and instructions). It is essentially the same old Designer updated to work with new concepts and files added to OH 2. It is missing some functionality, mainly it is unable to recognize stuff defined outside of the text files (e.g. Items created in PaperUI) and it is missing recognition of non-core Actions.
There is a new Experimental Rules Engine but for your purposes coding is done exactly the same with a few very minor differences, the main one being you no longer need all those imports at the top of your rules.
Right now text based config file editing using Designer is your one tool to rule them all. PaperUI and Habmin are growing in capability with every release but sitemaps are still not supported.
You can use the Free VisualStudio and @kubawolanin wrote a plug-in for it that can syntax highlight OH config files. I don’t think it does as deep and thorough a job of syntax checking as Designer but it does include the ability to insert code snippets and I know he has included a lot of the Design Pattern examples as snippets.
You can read more about it here