WDW vet here. From a WDW vet perspective, I would definitely get the hoppers. At DLR we often go back and forth between the parks all day. Unlike WDW where hopping is often an hour or more ordeal, at DLR hopping is a 5 minute experience. The distance between parks is shorter than most instances of getting off a bus at WDW and walking to the park gate. There is just a plaza between the gates. The bag check is on the outside edges of the plaza so you do not even go through bad check to hop. We have literally gotten from the back corner of DL to the opposite back corner of CA in 10 minutes. We hop a lot. For example, if the lines are getting long at DL in the afternoon, we look at the wait times on the app - we see the lines are much shorter on the whole at CA, so we hop over there awhile and take advantage of the shorter lines. We often do a day where we ride GRR at CA in the afternoon - get soaked and walk back to the resort to go to the pool and then have an early dinner at Goofy's Kitchen, and then go over to DL for the evening. If you like hoppers at WDW, you will love them at DLR.
As far as whether to stay on property or not- to us that is dependent on the money you are willing to spend and your WDW desire for the Disney bubble. We are so used to the WDW Disney bubble- that we really like to stay in the bubble at DLR. As a result, we like to stay at the
Disneyland Hotel, where it is a nice walk through DTD to get to and from the parks and resort and you never see the world outside of Disney property. Heck, if you stay at GC, you can walk straight into the CA theme park for the resort- the theme park room views there give new meaning to the term- there it means you look out your window and watch people walking down the path inside the theme park! There are lots of good neighbor hotels where you can save money and some even have a view of the theme park-- but you will be outside Disney property and you will be experiencing a regular (albeit touristy) street. If you decide to spend the money, we really do enjoy the Disneyland hotel. The rooms are nice, there is a character meal on property, the gift shop and Trader Sams are nice, and Goofy often shows up in the lobby. GC is beautiful too, but for us, it just feels like a scaled down version of Wilderness Lodge at WDW.
Have a great time!!!