Sensei Van has a very nice Underwood-----but wishes to know what is the best.
They are functionally all about the same. Keep in mind the last USGI version was built in 1945 so they are not new. Also, many were 'loaned' to other countries and may have well worn barrels.
The #1 thing to check is the bore and muzzle. It is imperative to have a muzzle ereosion gauge to check the condition of the muzzle. Anything over 3 will be a marginal shooter. I would not want a muzzle over 2 myself. Thru good fortune, my Winchster's bore measures under 1 on a USGI gauge and my Rock-ola at 1.5... both are excellent. Also, the bores must be bright and shiny. To check this a borelight is handy. Any pitting or corrosion in the bore should be a warning to you. Also, if the barrel was cleaned carelessly the muzzle could be worn out of round. Not a good thing.
Underwood was reported to make the best barrels but my Underwood measures around 2.5 and it is an Ok shooter at best.
For safety you need to check the headspace with quality gauges. Bolts get swapped over the years and an unsafe condition can develop as a result.