Level 1 Units

Initially, you probably could leave some units at level one. However, as game progresses, you will definitely need to upgrade or research.

What I will say is militia and armored cars, never good units, but can save you from angry AIs in needed in a pinch.

Base units mostly. If they aren't your country's doctrine specialty, I tend to maybe upgrade them once and maybe twice depending on the need but never more than that. For example if I'm playing as COMINTERN country I may upgrade SP artillery once or twice but I'm definitely maxing out SP rockets, cruisers, anti-tank, and maybe Heavy tanks.

Two of the biggest factors for unit upgrades past level 1 or 2:

1. strategy needed against your opponents

2. doctrine

I like doing militia (amazingly fast to produce) and (everyone will be shocked) mechanized infantry. Doctrine specific units probably should be research (medium tanks+mot infantry for axis, sp rockets for comintern, etc.