Loops are tough at Baxter and there is no commercial shuttle services that service the park (except for the AT lodge which is of most use to through hikers). There are two types of trails at Baxter, one type are the trails up the mountains. These really are far more suitable for day hikers as they are unlike anything you might find in PA. They are steep rough and rocky and overnight backpacks are not really recommended for first timers. The other trail run in the valleys which gives a hiker to the remote campsites and many lakes and ponds. Unfortunately they tend to be "out and back" via the same trail if you want to end up at your car.
I would suggest that if you can get reservations at Russell Pond it may be the ticket. Go to the website and look over the hike planning section and download this map
https://baxterstatepark.org/wp-conte..._28mar2017.pdf. Russell Pond is strictly backpack in there are no roads. Unlike the trails to the summits, there is very little traffic on these trails. The tents sites and shelters are circled around a large very wooded pond and are well separated. There are resident moose and you are just as likely to encounter one in the evening as another person camping there. The only down side is the water source got ruined by beaver and therefore you need to take it out of the pond. A filter is recommended as chemical treatments don't take out the pond taste. If this place is too busy and you want more privacy there are a outlying shelters managed by the Russell Pond ranger where you may be the only campers for miles.
https://baxterstatepark.org/wp-conte...SP_20Apr17.pdf. The two shelters on Wassataquoik Lake and the Center Pond Shelter are very private. The two Wassataquoik Stream Shelters are in a great place but you will have a neighbor. If you are into big miles you may be disappointed but there are all sorts of places to day hike in the Russell Pond area. A possible itinerary is drive to Roaring Brook campground, then put on the backpack and take an easy hike to Russell Pond with a few detours. Take the trail around Sandy Stream Pond to check out the view and the resident moose with Katahdin in the background. Consider hiking up South Turner mountain with your backpack ( I wouldn't leave it at the base or the critters may raid it) The view of the East side to the Katahdin massive from South Turner is hard to beat. Now head down south turner and take one of two trails, either the Russell Pond Trail or the Wassataquoik stream trail. Note there is no bridge over Wassataquoik Stream and if you have to ford it after a rain if can be waist deep and cold. The Russell Pond trail has some wet crossings but nothing as substantial. Now it comes down to where you could reserve a site. If you are moving fast with no stops you can go between Roaring Brook and Russell Pond in about 2.5 to 3 hours so take your time. Wassataquoik lake its 45 minutes from Russell. Russell has a couple of local hikes while the lake has fewer. Some folks would just head in for two days and head out. This area is about as remote as you can get in Baxter, the stars are incredible as the sky is super dark.
Note I really don't recommend trying to overnight backpack over Mt Katahdin, people do it but for first timer definitely not recommended. I would suggest if you want to climb the mountain head out to Russell for one night come back to Roaring Brook for an overnight and then do a day hike to the summit from Roaring Brook via Chimney Pond Trail, Cathedral Trail if you are brave and then down via Saddle of Hamlin Ridge trail (Hamlin ridge trail makes for long day). I would do this on the last day of your trip as you will be beat and not in the mood to hike anywhere the next day.
So now what you need to do is go on the reservations system now and see what sites are open on the dates you plan to visit. If you are going to Russell Pond you can reserve individual sites. Leanto #5 is the most private but sits back from the pond a bit. The woods are very dense at Russell Pond with the exception of two canoe docks so it looks very wild.
There is also one of the rare loop options in the north end of the park in the Scientific Forest Management Area. This area is managed for sustainable wood production and is less wild than the rest of the park. There is loop using the Wadleigh Brook trail to the Hudson Pond Shelter for the night. Next day head north to the Freezeout trail and hike along Webster Brook to the Little East Shelter on the shore of Grand Lake Matagamon the south to the Frost Pond trail and back to where you started the next day. This is classic Maine woods, not a lot of views. I haven't hiked it and in early season it could be more buggy than the rest of the park.