When to worry about engine noises?

There is a lot of superstition and myth about oils as most people don't know what is in an oil or how they are certified. Also, times change, and advertizing of the past doesn't apply to current products. Such as Pennzoil sludges your engine or Mobil 1 Synthetic is superier to other oils. These are myths.
Modern engine oils meet API requirements which include multiple engine tests designed to stress oils to the limit of engine operating conditions (extreme heat, long duration slow speed operation, e.g., Taxi service, high engine speed, etc). Essentially all modern engine oils are formulated with base oils that are functionally equivalent to "synthetic" base oils and many meet the defintion of synthetic although they are not the specific synthetic molecule used by Mobil. What is far more important is what engine tests and certifications the oils meets, and will it protect your specific engine.
Engines with roller follower camshafts can use the latest API classifications such as SN and just released SP. Engines with slider follower camshafts (most pre-1980 engines) need additional ZnDTP (antiwear additive). You can buy an oil that claims this but it won't meet current API requirements so there are risks. Or you can buy Heavy Duty Diesel Engine Oils that display both the C-category (CH-4 and the like) and the S-Category (SN or SP). Only HDDEO's are allowed to have higher ZnDTP levels as there are diesel engine components that require the additional antiwear additive.
I ran Delo 400 SAE 15W-40 in all my engines since 1981 when I began formulating for Chevron and their additive company Oronite. I ran it in a freshly rebuilt 1966 426 Hemi Belvedere, 1967 Barracuda 383 Formula S, 1970 Challenger R/T 383, and my '68 Barracuda 340 Formula S. I raced all but the Hemi multiple times and never had a lubricant issue.
Formulating engine oils requires about $2 million in engine tests and most additive suppliers also conduct field tests. In my experience with formulating oils, I found that there is essentially no meaningful difference between conventional hydroprocessed and synthetic oils other than cost. I formulated an ancient engine oil with less than half the additives of modern oils and tested it in NY City taxicabs for 100,000 miles. Modern oils had a 10,000 mile drain interval and the older oil was changed at 3,000 miles. The engines were disassembled and measured for wear and deposits. The old oil with 3000 mil drain showed less wear and deposits than the modern oils with 10,000 mile drain. This demonstrates that it is far more important to change your oil than worrying about which oil you use.
I would recommend using a modern oil with additional ZnDTP additive than use an oil that does not knowing what specifications the oil meets.
I will use Delo 400 SAE 15W-40 in my new 340 engine that will be started in about a month once the interior and exterior are assembled.