Personally I'd use a good polyurethane paint dilute the first coat 20% with thinner or add a penetrating paint addiditive (penetrol) this will generate a better bond allow the paint to cure TOTALLY before using it. The best is to 'bake' it. If you can place it in a warm (100º) area with really good ventilation that will force the thinners out faster and more efficiently. The best test is your nose if it still smells 'painty' it isn't done. It will take awhile 5-10 days. I would not use a floor product as they are designed in many cases to hold elasticisty and the often out gas for a longer period of time. NEVER use a spar varnish they are very soft (boat masts move a lot) and never completely out gas.
Kiln dried pine has most of the phenols baked out of it. Use your nose if it is very piney smelling pick a different bit. But in any case polyurethane cured is plastic if you paint the whole rack it is encapsulated in plastic. The phenol gas will not penetrate the plastic. There is also debate about pine anyway so as I feel it isn't worth the risk to use as a substrate there are very respected keepers whom use kiln dried pine as substrates. The only wood I would not use is cedar. As it isn't a good choice anyway it makes no difference.
You can also sometimes find poplar boards in some lumber yards it is very soft wood but works like pine. It is an odd look greenish brown and is never found very large so it means lots of glueing. It has almost no phenols. (is also know as Aspen)