Staying at the GCH is amazing. I have only stayed twice (both times 2 nights each) and both times was great! Depending on where you are in the hotel, you can be a 2-5 minute walk from your hotel room to inside the DCA. The first time we stayed and I counted 47 steps from our elevator to the private park entrance. This can be especially helpful for those with littles (and bigs) who may need a nap or rest. I love getting EE (early entry) for every morning of your stay. This is especially nice at DCA, where only DLR guests have access. At DL guests who get a 3 day park hopper get one EMH for their stay, so it can be more crowded when access EE at DL
I will be honest I have stayed at all three onsite hotels and like each for different reasons. The grounds and pool at DLH cannot be beat and I love the displays at each tower, and Traders Sam’s, need I say more? Paradise Pier usually has the best price, although it is the furthest away and the most inconvenient of the “on-site parks.” I do like the brightness of the rooms and the amazing views of DCA. To get the most “in the bubble feel” GCH is your best bet IMO, So if it is in your budget, I say go for it.
Many of the DLR regulars say that there is not as much of Disney bubble feel as there is at WDW, but for me it was the opposite. I think for me, having to travel so far to go from one park to another, it felt like I was going to a different park/resort. Having everything so close together at DLR gives me that “bubble” feel. It is different for everyone I suppose.
As far as when, traditionally to avoid crowds, I would say early September or early November. Take into consideration that some rides may be down for holiday overlays though. We had a great trip this last year the week before thanksgiving. The crowds were manageable and we got to see DLR decorated for Christmas, which is my favorite time of year there (Halloween is a close second). I normally won’t ride IASW, but after dark during the holidays it is a must do!