A big factor in price is the quality of components. For a ride this long, don’t skimp. Yes, that bike with the “sora” shifters is several hundred dollars cheaper than the one with the “ultegra” components, but the time you spend adjusting and being frustrated with the improper shifting will likely make you regret the cheaper option.
Higher-end component groups are also lighter than typical Sora priced bikes. At a minimum, go with Shimano Deore/105 or SRAM Rival as your component groupset.
All bikes have a set of gears on the back wheel (the rear sprocket), as well as a number of gears in the front (the front chain ring). The days of the “ten-speed” (two in the front and five in the back) are done. These days you usually have 8, 9, or 10 in the back, and two or three in the front. But in addition to the numbers, the size of the various cogs and rings can have a big impact on your ride.
In the rear sprocket, the smallest cogs are for riding fast, and the biggest cogs you use when going up hills (it’s the opposite in the front: the big ring on the outside is for going fast). Some rear sprockets have a broader range than others. Generally speaking, hybrids will have a broader range than cyclocross or road bikes.
On the front, triples have an extra small ring (granny gear) for going up steep hills. Not necessary on this trip, in my opinion, but doesn’t hurt. Notice that true cyclocross bikes have two rings that are very close together in size, which is also not needed on this trip.
It’s a long ride, so having a proper fit makes a big, big difference. Go to a good bike store where they truly understand fit (in other words, not a big chain). You might spend a few more bucks on extra components to make the bike fit right (or thousands more on a custom made bike), but with this much pedaling, if your angles are off, or if your seat is too high, or your bike cleats are not properly aligned, it can cause you some serious pain and discomfort.
You will spend about $200 for a bike fit. You can try and fit yourself to your bike but unless you know your way around a bike, geometry, and your body - leave it to a trained bike fit professional. Fit is especially important if you gained or lost weight or gained or lost flexibility. Make sure the professional performing your fit gives you the measurements and check them every quarter to semi-annually. If you’ve never been fitted to your bike, look at it as an investment in ride comfort and faster recovery.