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Hitch Size: 2" vs 1.25"
(lemmy.world)
Using a hitch safely involves being mindful of the "weakest link" in the whole assembly, from the accessory's limits, to the hitch receiver's weight class, to the vehicle's abilities and caveats. An optimized setup will balance those factors so you're not wasting money on something that is limited by something else.
When you say hauling bikes, I assume that means at least two or more, since a single bike carrier is generally A-OK for any hitch of any size, on any car that U-Haul is willing to install a hitch receiver on. However, carriers for two bikes are often available for 1.25 and 2 inch. If you want to move more than two bikes, 2 inch will give you a lot more options.
The caveat is that this assumes the bikes are normal bicycles, like road bikes or adult mountain bikes, as many dual-bike carriers have a maximum weight rating of 70-90 lbs (30-40 kg) total. Going up to a 2" carrier doesn't necessarily increase the weight rating. Ebikes can really push the limits of multi-bike carriers, which may not be built to accommodate a single, heavy bike.
My suggestion is to look at bike carriers now, while considering if you will want to expand to more bikes in future. It may be that your area has 2" bike carriers for cheap on FB Marketplace or Craigslist, and that will tip the scales toward 2". On the flip side, 1.25" carriers tend to be lighter and easier to install. Since you plan to get a bike carrier anyway, might as well include this in your decision of 1.25" vs 2".
IMO, if your car can have a 2" hitch receiver, then you should take up that option as it unlocks a lot of potential for your car, whether you use it for more than bikes or to just increase your car's resale value.
As for "hidden crossbar", my guess is this refers to whether more of the hitch receiver is visible than the square slot. This would mostly be down to aesthetics, but could also have an implication on ground clearance. Best to clarify with the U-Haul folks about this.