The oiling system is poor only if you spin the motor at high RPM. If
this car is just a cruiser or driven lightly, the oiling sytem is fine.
The "poor" part about it is that the main bearings are not oiled first.
They get oil after other parts of the engine get oil.
10W-40 oil is fine, but the more difference between viscoscity, (in
this case, the "10" vs the "40") the greater the chance that your
engine will have deposits and varnish. If your engine has no leaks and
doesn't use oil, 10W-30 will be fine also. They do make some synthetic
10W-40, but it can be hard to find. If you don't put too many miles on
this car, the benefits are questionable.
There are some oiling modifications that can be done to this engine to
improve the oiling system, but I wouldn't do it unless you are really
going to rev this motor.
Any oil that now has the SL or SM SAE rating would be fine.

Unless the engine has a recent rebuild (~10,000 miles) then stick with dino
oil. I only used 20W50 for break in on my 351W stroker last summer in
August. It's too damn thick and even though it's more heat resistant, it
takes FOREVER to get pumped to the top of your motor, causing way more
damage than just using a lighter oil. I drained the 20W50 at 500 miles and
switched to 10W30 for the summer. At 10,000 miles I'll switch to 5W30 Synth.

Is it really only 40F in the summer in Chicago?  If it's that cool, I
would use a 10W.  20W is too thick for cold starts in cool/cold
weather.  And 10W-40 has more additives to get that wider viscosity
split, and more additives means less oil/lubricant.  So, I'd go with a
10W-30.

As for synthetic or conventional, go with what's more important to you.
If the motor is really solid, then it's probably worth the extra bucks
to dump in synthetic.  But if the motor has some miles on it and will
probably need a rebuild in the near future, then don't waste the extra
cash, use conventional.   If it's just an average decent motor, but
nothing great, then mix a couple quarts of synthetic in with the
conventional to save a few bucks.        

Patrick
'93 Cobra