Also, does this Oculus Store need to be running all the time just to use VR? I understand there being a VR app, but why does it have to be an entire virtual store using precious RAM and CPU cycles instead of a simple driver software?
Because they're more interested in selling you stuff than they are in your computer's efficiency.
Having said that, it's very easy to set up a window on to your desktop in Oculus Home. This is particularly handy if you're using spansh to traverse the Neutron Highway. Open spansh on your desktop and make sure you can see it in Oculus Home.
Then when your jump starts pick up a controller, switch to Oculus Home, click the copy icon beside your next star in the route on the spansh website, press the button on the controller again to return to the game (you may find the game doesn't have focus - I have Voice Attack set up so that I can press a key to return focus to the game, but I believe there's an AutoHotKey script that will do this if you move your joystick) and your next destination is ready to paste into the Galaxy Map - I actually have a Voice Attack macro which has one of my joystick buttons open the Galaxy Map, move to the text entry box in the second tab, perform Ctrl-V, then move to the selected star. If doesn't go as far as plotting the jump because sometimes I want to jump to an adjacent fuel star.
You can also look at other external sites like eddb. But be warned that a controller makes a lousy substitute for a mouse, though it's not totally unusable.