OP, I agree with others that purchasing a lightly used Class C is a great way to go. The newer and nicer that it is (and that you keep it), the more it is worth for sale next spring if you decide the lifestyle isn't for you. Class A tends to be more expensive than Class C. I think you are more likely to find a newer used C than A, because rarely do newbies buy a Class A and decide they don't like it and sell it relatively new.
Just a suggestion, look for a Class C with either a toad included, or a Class C that is setup for a toad if you have a car that you plan to take with you. Buying the rig already setup will be cheaper, easier and allow you to hit the road faster.
Class B is SMALL. For a weekend trip, they are great. For a minimalist couple, it might work for 3-4 months, but I wouldn't like it. If it rains and you are both jammed in a small van for a couple days, its gonna get REALLY small. If you have to be in/around the rig for work most days, its gonna get really small. Benefits of a B include better mileage and no need for a towed vehicle... but if you are working from the camper and the spouse needs to go to the store... what are you going to do? 4 months with no second vehicle will be quite annoying.
I think a 26-30 foot A or C with a slide would be ideal. Small enough to fit in most places, small enough to more easily drive, but large enough to provide creature comforts for a 4 month trip.
One other option is to buy a used truck and trailer or fifth wheel. Might be harder to find that kind of rig for $50K, but if you need or have a truck anyways, you are halfway there!
In terms of NY to FL to CA in a couple months, you'll be fine! When I was younger we did a family cross country trip in 6 weeks. Maryland, down south, across west, up north, back east, down south slightly, back up north and back to Maryland... in 6 weeks... in a van... and 26 foot non-slide bunkhouse... with 2 sisters, the parents and a dog.
4 months to do all that should be fine. That should be plenty of time to explore, see the sights and have fun. $15K spending money seems like a good estimate. Hopefully its high, but fuel, food, groceries, site fees, incidentals, etc can add up. You are giving yourself almost $4K a month. I think you can do it for less than that, but its probably a good place to start your budget.
I agree with Verizon MiFi. Verizon has the best coverage across the country. Be prepared that some days you won't get signal. Be prepared that "free WiFi" at campgrounds is likely to be spotty at best.
Good luck on your decision and hope you have a great time! I wish my job afforded me the ability to take on an endeavor like this!!!
