Nothing wrong with towing with your F-250, that is a nice safe rig with plenty of extra capacity for gear in the truck bed. 

The hitch options you are referring to are (1) a weight distribution hitch (wdh) which re-balances weight from the rear of the tow vehicle to the front axle improving handing and braking and (2) trailer sway control which minimizes the likelihood of the trailer sway. 

You shouldn't really need a wdh with a F-250, it can handle a lot more weight than an rPod, unless maybe if you also put a full ton of stuff in the truck bed. Up to you but I'd skip it and see how you like towing without one. 

The most important thing to do to prevent trailer sway is to be sure you have enough weight on the trailer tongue. For an rPod that should be 10% of total trailer weight at the very minimum, preferably more like 12%.  You have to weigh the trailer and tongue (fully loaded including water if you plan to boon dock) in order to know that, which you can do at a public scale. Here's why:

https://www.google.com/search?q=trailer+sway+video&oq=trailer+sway+video&aqs=chrome..69i57j0i22i30l3j0i10i22i30j0i22i30l2.4407j0j7&sourceid=chrome&ie=UTF-8

Even with a well balanced trailer, sway is still possible, so I would suggest still getting sway control even without a weight distribution hitch. The lowest cost option would probably be something like this. 

https://www.amazon.com/Pro-83660-Value-Friction-Control/dp/B0016KJ5MC/ref=pd_lpo_263_img_2/140-2048306-1226438?_encoding=UTF8&pd_rd_i=B0016KJ5MC&pd_rd_r=76cf10f8-282d-4f8d-a47f-6e28a4b3f41e&pd_rd_w=6B9YR&pd_rd_wg=OzOSQ&pf_rd_p=7b36d496-f366-4631-94d3-61b87b52511b&pf_rd_r=44Y4SBXDHMRXQ9VDY068&psc=1&refRID=44Y4SBXDHMRXQ9VDY068

https://www.amazon.com/Reese-26003-Sway-Control-Adapter/dp/B0008F68MG

Or you could get one of the electronic sway control systems that senses sway and activates the trailer brakes, but those are quite a bit more expensive. 

Congrats on having a tow vehicle that will have 'towing authority' over the trailer. As you learn to pack for a long trip, try to load heavy items like jugs of water, generator, cases of canned food, gas cans, propane tanks, tool boxes, etc etc toward the front of the pickup bed. This will add stability and shift weight from the trailer to the tow vehicle.

You will need to add a brake controller, if your pickup is not equipped with one. 

I have had no incidences of significant sway, even on I-70 in western Kansas where we encountered 30-50 mph cross winds for hours and semis passing us at 85.  I keep it at 65mph or slightly less.

I bet your 3/4-ton will handle the 176 just fine as long as you don't start chasing the speeders...

I plan to pick it up on Thursday, and then head off straight for week trailering.  Since I'm picking it up 200 mile from our home all our camping stuff will be in the truck bed in tubs.    Based on what you say as long as I make sure I have tongue weight is at least 10 % of GVW of trailer we shouldn't have a problem.  

Maybe long term a sway controller makes sense.   But for this first outing should not be a problem without sway bars. 

Keep on RV

Bear in mind that in the 176 the water heater, fresh water tank, and pass through storage areas look like they are behind the trailer axle. There is nothing in any of those in Forest River's published weight data, so if you load those up you will be reducing your tongue weight. Not to sound like a broken record here, but do get actual loaded tongue and trailer weights to be sure. 

One is to get a a tongue weight scale like this:

Then I disconnect the trailer and go back through the scale to get the weight the tow vehicle by itself. The difference between the combined rig from the first weighing and the second weighing is the trailer weight. The difference between the weight of the two tow vehicle axles from the first weighing and the second weighing is the tongue weight. 

Often you can do this for free at your county waste transfer station. Go at a quiet time of day and ask nice. 

If you want to proceed you can get a bracket to mount the anti-sway friction bar offset from the ball, like this. 

https://www.etrailer.com/p-RP26003.html - https://www.etrailer.com/p-RP26003.html

There is a photo on that web page showing how the bracket gets mounted on a drop down hitch. 

Its really a personal choice about how much risk you want to take. To me getting the weights right and then adding either a wdh or a friction bar seems to be a good place, others could choose differently. With a heavy tow vehicle like your F250 you can still get trailer sway but it would take quite a lot to also get the TV to decide not to stay planted. 

BTW, if you have the time and presence of mind, applying a bit of trailer braking using the manual control on your brake controller will bring the trailer back in line behind the tow vehicle. Probably it goes without saying but you never want to apply your TV brakes if you do get trailer sway, unless of course you'd like to get a good view of your trailer proceeding you down the highway. 

https://www.hitchweb.com/blog/post/2013/01/07/how-electric-brakes-work - https://www.hitchweb.com/blog/post/2013/01/07/how-electric-brakes-work

The brake controller outputs a voltage that varies depending on how much braking action is needed. In modern controllers that voltage is proportional to the rate at which you are slowing the tow vehicle down so the trailer brakes are following along with how aggressively you're using the TV brakes. 

You will have a couple of adjustments to make in the controller setup which usually only has to be done once unless you change trailers or really change the trailer loading a lot. The other thing you will want to know how to do is how to activate the controller manually so you can test the trailer brakes without operating the tow vehicle brakes before hitting the road. Otherwise it can be hard to tell if the trailer brakes are working because the TV brakes have much more capacity.