I have Cubase Elements which is similar to Cubase AI, so I might be able to help with that. I also have the "free" version of Ableton-- Live Lite-- which comes bundled with certain audio or MIDI equipment. Cubase would be more powerful than Live as far as being able to handle any MIDI-related stuff (Live doesn't handle MIDI SysEx at all, but Cubase does). However, my personal favorite DAW for playing virtual instruments is Acoustica Mixcraft (which also does not handle MIDI SysEx), because I love how easy it is to create layers and splits with Mixcraft.
There are also programs that are specifically designed for managing set lists and patch changes for performing keyboardists. The one that I keep hearing the most love about is Cantabile-- or, if you're using a Mac (which I know you aren't), then MainStage gets a lot of love. I have the free version of Cantabile, but I haven't explored it yet, and I think you need the Pro version for the more powerful features.
But just about any DAW such as Cubase, Live, Mixcraft, Cakewalk, etc. should be able to let you do what you want as far as being able to play virtual instruments.
Once you've gotten past the part about connecting things together and setting up your DAW or other plug-in host (which really isn't that difficult, just a bit bewildering), you'll want to focus on which virtual instruments to get, unless your DAW comes with some that you're satisfied with.
Another possible issue will be whether your laptop is powerful enough to handle the virtual instruments (VIs) without any hiccups, especially if you plan to use multiple VIs at once.
I don't want to try to dissuade you from using DAWs and VIs, but in the long run it might be best to make some sort of spreadsheet or list of patches/programs you like to use at home on your MOXF8, and the closest ones on the Juno-DS. They won't sound exactly the same, of course, but you might be able to gradually build up a series of patch files to use on your MOXF8, and equivalent patch files for the Juno-DS. You could start with a few for the most common "generic" voices, such as Acoustic Piano, Church Organ, Clarinet, Flute, Trombone, etc., and then develop a collection of more song-specific patch files for whichever hymns or inspirational music you'll be playing.