Moosh and Wander

A new motorhome should ride and track correctly BEFORE it rolls off of the showroom floor. A thorough test drive will reveal any inadequacies which are, at that point, the dealers problem. New C's should not require thousands in additional equipment to insure a decent ride. If they do you are buying the wrong MH. :S

I suspect the OP's coach needs some adjustment to its tire pressure and perhaps an alignment. As noted a little more castor can often work wonders on the handling. A trip to the scales is warranted here so that the tires can be brought to the proper psi. At 55 psi (in the Michelin LTX M/S 2's), all around our 24' C (E-350), rides smooth and quiet with no handling issues whatsoever. :C

First thing I wanted to do was look up the Wheelbase of the 28z and what I found was 210-inches. With an overall coach length right at 30-feet. I believe your coach DOES have the possibility of enough Front Axle Weight to be able to get it to track well AND keep the Rear Axle Weight under its maximum. You'd be surprised how many Class C's cannot accomplish that. Their WB is too short to balance the rear overhang against the weight of the rest of the coach.
OK, So What? Load it up as if for travel/camping trip and weigh it. As mentioned, Truck Stop CAT scales will give you Axle Weights. If you tow a vehicle, have it in tow. You'll get the Coach Front, Coach Rear (called Steer and Drive on the CAT report) and Towed Vehicle (called Trailer). Have that Load/Pressure Chart with you and adjust tire pressures accordingly. Check and adjust all six. Some of us have found For-Sale coaches, even new ones, with the tire pressures all over the board.
See how it drives, and please report your Axle Weights to us.
If you aren't satisfied with what it's doing, get it aligned at a truck shop that understands Ford E-Series. There's more to doing a Twin-I-Beam Ford than an 18-wheeler with a big I-Beam front axle. Tell them you want at least 5-degrees CASTER. They should say "You'll need Offset Bushings" to which you should say "Correct."
I installed upgraded Front and Rear Sway Bars (Hellwig) and Rear Track Bar (BlueOx). They improve the conditions they're meant to address but doing those first would be like putting a broken bone in a cast before you XRay and set it.
Again, let us know how you're doing.

As has been stated weigh it as if it was loaded for a trip best if you can get s weight for each of the four corners but at least for the front and rear axle besides the overall weight. Besides sitting your tire pressure you need to see if you have at least 80% of the front axles rated weight if you do not you can have handling issues. All weight behind the rear axles will take weight off of the front so that is why it so important when you weigh it you have it loaded as if you were going on a trip including yourself and passengers riding where they ride when traveling. Then if you still have handling issues alignment. IMHO always do the simplest cheapest first

Before adding any after market things to it, get the alinment checked. The best place is a Ford Truck dealer. Then see how it feels.
I've never added any after market things to any of our mh's but I'm used to driving a Ford Van, E-150, any way, they do drive a little different.

Dusty

Once you get the right tire pressures, get the front end aligned. It will stop the wandering!

Yes..

Every time mine has gone in to service including the latest Michelin recall, the tires have come out being set at 75 PSI or more--front and back. Even when I asked for specific setting. There is only a small contact patch on the front tires on my motorhome when set at 75 PSI. On my 24' the front end weighs about 3700 calling for about 50 PSI. At that point I start to see a decent contact patch.

As was stated earlier the first thing you should do is weigh your MH.
Set your front and rear tire pressures to what this schedule calls for. That alone could solve your issues. My 32 1/2' MH runs as if on rails, with no need for any add ons.

Ditto on checking tire pressures, especially the front. Don't go with what is stamped on side of tire.
At least set all tires to what the MH manufacturer has on there placard, best to get it properly weighed and then check with the tire manufacturers website for load inflation. Michelin inflation.
With ours the placard agrees with the weight and Michelin, 65 psi for the fronts and 80 for the rears. Our fronts have been aired up to 80psi at times and the handling is terrible, when decreased to 65 - 70 (fronts only), it drives like a totally different vehicle.
All tire pressures are done when cold (ambient temps), before driving.

Beverley and Ken

Sway bars helped mine. I didn't do shocks but mine are borderline inadequate on a "lightweight" 24 footer.

Off the bat, weigh the rig front and rear and set tire pressures to the weight (mfg should have a spec on that). You don't want front tires overinflated. Try to shift weight forward when possible (not heavy in overhead cab though).

Dig through the posts here in the C forum, looking for member Harvard and his thoughts on caster. He recommends maximum caster under the Ford spec, not the intermediate value. I would also recommend a tad of toe-in, not the zero degrees recommended by Ford. I'd go to alignment shop with specs in hand you want it set for.

These things will never handle like a million bucks but they can be a lot better. They're never a lot of fun to drive in windy conditions. In general getting used to it will help, and I think they feel a little more buttoned down when the tires wear in a bit.