Is this the one pictured below?
You are right that the 4cyl on that Santa Fe and its suspension won't handle this trailer.
The easiest recommendation for a tow vehicle is to buy a vehicle that can tow 6,000lbs (4770/80% = 5,963lbs) or more. That would more
than cover towing this trailer. But, might also be overkill and take you into a larger vehicle than you want.
Are you familiar with towing calculators? Most people use them to verify that their new trailer will work with their existing vehicle or to see if they are overloaded.
You, on the other hand, are in a nice position that you intend to buy a new vehicle to fit your trailering needs. You can play around with one like this to get an idea of what tow ratings you will need.
Assume that the tongue weight will be 550-600lbs and not the 370lbs they list in the brochure.
Travel Trailer Weight Calculator