Wow, the car my Dad bought when I was born the next to the next to the last day of 1958!! Tax deduction for a child was realistic way back when. They had it until 1966
. Green & white, with a SEARS A/C underdash unit added almost immediately (and that never needed a Freon re-charge).
Towing puts quite a strain on all suspension and steering "rubber". From body and sub-frame bushings, to leaf bushings and torsion arm bushings to the steering rack "ragg" joint. Those were the first order of business I attended to when I inherited another family car, a 1971 Chrysler. After that were completely new brakes. (And I would not tow anything with a single cylinder brake master; I believe upgrades to better systems are available; the 1965-1973 Chrysler vehicles all could use 1971 and later single piston front disc / rear drum systems with dual cylinder, for example).
Steering or front end slop is completely unacceptable in a tow vehicle. Adjustments can be made (mechanical skill needed, but experienced at adjusting a box is better).
There was little to none towing information available at that time of the type we take for granted today. Hitches were pretty much all custom. Chrysler began providing blueprints for hitch building at some point in time relative to that (mid-1960's forward).
an example. Diagonal cross-bracing also recommended. (And pull the gas tank and replace or carefully overhaul it now: new lines, etc. An "pusher" CARTER fuel pump added at that location an excellent upgrade to help prevent vapor lock; internally-regulated.)
And, what "overloads"? Extra spring pack? (rear of the car sits too high)?
As to what you can tow, only your wallet will decide. An aero all-aluminum trailer up to 5,000-lbs won't be any problem given the proper hitch rigging (and better brakes for the tow vehicle), best brake controller, transmission & power steering fluid coolers/filters.
The car's cooling system needs to be about perfect (thermostatic control fan clutch and good fan shrouding). And I'd also convert to a modern internally-regulated alternator (post-1970) were it mine.
Rear axle ratio is another concern. 2.73:1 is great for solo car highway. 2.94:1 (the Imperial ratio) is better, and the Chrysler towing package axle ratio of later years (to the late 1970's) was 3.23:1 (which would be my choice). It's a fairly simple change-out due to the axle design. The engine and transmission will have a much easier life with numerically higher gears (and around town mpg can also improve).
Be sure to have the bands adjusted on that T-flite when a fluid/filter change is done. And have a rear axle bearing service and re-pack done (tapered roller bearings not
lubricated by the axle gear oil (superior design, but unfamiliar to Ford or Chubby owners).
That engine -- with it's leaded gasoline requirement -- will be okay until one day it isn't. Valve recession is a real deal on a car asked to work . . and towing is work. Rebuilt stock heads, or a possible swap to -346 1971 or later cylinder heads will be wanted. The carb may or may not be problematic. An Edelbrock AFB clone is fairly simple to set up if wanted. A single exhaust pipe system is adequate if one follows Chryslers design: 2.25" downpipes to 2.5" main to muffler then 1.78" to tip. No crimps, specify mandrel-bent pipe.
My choice of oil would be Shell Rotella T6 5W-40, and a WIX filter (or NAPA Gold) as both are reliable and easy to source.
I'd also convert to MOPAR electronic ignition. Be sure to check for timing chain slop. A CLOYES double roller is a good upgrade (and be sure harmonic balancer rubber not rotted).