Background: I'm familiar with animation/modeling, but rather new to Houdini. Before Houdini, I only used Blender and Maya, and all my animations are rendered with Eevee/Cycles in Blender.

There are so many renderers for Houdini, but I don't know which to choose. Is Mantra going to get replaced by Karma? Is there any advantage to buying a third-party renderer like Redshift/Vray/Octane over Mantra/Karma? If so which one?

I know I can export from Houdini and just render in Blender. But from my experience of Blender, being able to make changes on geometry and see a preview of final rendering in the same software is very valuable and speeds up the look dev drastically. How do Houdini people generally do this?

I'd go with 3Delight to start. It's free for commercial use up to 12 cores. Very fast and easy to use, great Houdini integration. Should be an H19 build coming soon. Skip Mantra. Karma is very nice now, but it involves using Solaris which is just another thing to learn.

Forgo Mantra as it will surely become obsolete in a couple of versions, and it's really slow, use Karma, and yes it runs inside Solaris(USD), which is another thing to learn, but it is very powerful and it allows you to use the lookdev stuff, is a great way to manage assets and scenes, and much more, and if you use an external render engine you will also need extra steps for many things, like rendering oceans, which would involve exporting maps and setting up shaders for the external renderer, so on and so forth, also you need to learn Solaris for some of the new stuff, like the layout node!