I haven’t accessed you link so I couldn’t advise you on the hostels, but I’ve done some searching before, and they usually include some information on the nearest RER station.

You can opt for the tourist day pass 2,3-day passes, available at major stations. This you can use for all public modes of transport such as buses, metro,etc, except taxis.

I suggest you familiarize yourself with the bus routes as well. Since you know where you want to go, plot it in the map against the bus routes and hop in and hop off the bus if you stop near the sights you want to see, this is cheap and enjoyable albeit tiring.

Make sure you get the right pass, since you could be charged a huge fine if some inspectors show up for a spot inspection of tickets and you don’t have the correct pass with you.

The places you want to visit are near each other and manageable to maneuver via bus routes. Make sure to visit the sites both in day and night. The lights are amazing at the champs elysees and of course eiffel during night time.

Be safe and enjoy!