I'm not sure on the others but I don't believe var veitchiana is a correct ID for any of those. Way too much pink in the petals. Mine is almost white w/a lavender lip that is almost coerulea in color. I can't find my pics right now but
HERE is a great example. I got mine at Andy's but it looks just like this one.
My gouldiana is in spike right now...as is my anceps 'Greta Garbo' and autumnalis...I can post pics when they are in flower.
As for the root growth...anceps and the other ancep types/Mexican laelias produce roots after they flower. The new growths get started...grow and mature and flower...and then the roots begin to grow. I think I've had a couple of occasions where one or two might have started roots toward the end of the flowering but that could just be a mis-remembered thing. As a general rule w/these guys...no roots until flowering is finished. And, if I'm not mistaken, there is a period of inactivity prior to the roots actually starting to grow. I'll have to pay more attention this year.
I have some mounted and some in pots...they grow equally well for me. As long as whatever it's potted in can dry fast, it'll be good. My mounted ones have become quite cumbersome for a home growing set up and I recently divided the var veitchiana...cutting the front section off and potting it up. If you have the space...they will all do very well mounted and you'd never have to worry about accidentally rotting the roots by watering too much in winter.
FWIW - I do most of my watering late afternoon but my space is very dry due to the lights so I do this on purpose so the water doesn't evaporate before it has a chance to actually give the plants some hydration.