Airline for Travel to CPH

From where?

an airline that's legit to Copenhagen

What does this mean?

Norwegian has just announced that they are cutting all long haul routes to/from Copenhagen, so they might not be the best choice. But SAS has direct flights from several US cities. From Canada, Air Canada has direct flights from Toronto.

My apologies for not being clear. We'd be departing from Austin or San Antonio TX.
We want to spend one week in Denmark and one in Netherlands, both ancestral origins for our recent ancestors.

Just wanted to know if there v are certain airlines from US that we should avoid - like the lesser known big ones. Trying to get good prices and reliable carrier.

Finding "best" air travel takes a bit of work. What is "best" may be different for different folks. Best may be price or may be schedule, or for some best is the airline that they have been accumulating mileage awards. In the past some travelers would pay the travel agent premium to do the work to find the best.

For a DIY approach, I would start using a travel search engine (e.g. https://www.travelocity.com/Flights ) and test out travel routes. That is find what is available departing Austin and San Antonio to CPH and return. If you have DFW area friends (good friends) consider driving to DFW and departing from there (leaving you car with your good friends). Recheck prices using the preferred airline's booking system.

In terms of reliability, I would be cautious about discount airlines that do not have daily flights. First, they may drop the flight's city pairing. Second, if there is a cancelation/delay or missed connection problem, they may not be able to accomodate you on the next flight. I use a flight tracker like https://flightaware.com/ to check on the delay and cancelation record of recent flights. Note that seasonal weather can have a big impact on flight performance.

Do some trials google.com/flights, this is not a site that sells tickets. I did a couple trials, it looks like prices are substantially less if you fly from Austin, to Copenhagen, and back from Amsterdam (no backtracking). We are talking in the United/Air Canada/Lufthansa group with only one plane change, this was in June on Tuesdays.

In that case, book an open jaw ticket and fly to Copenhagen and home from Amsterdam (or vice versa).

In general, avoid any US airline and choose a European airline instead. They are in general slightly better and flying a European airline means both your flights will be EU261-protected.