Don't take this the wrong way, but if you want to completely eliminate all wood grain and paint a gloss finish, why not use MDF, or even a solid acrylic? Both can be worked with the same tools and would be much less work.
Grain filler is good if it is open grained wood. For the most part priming and sanding the primer between coat until the finish is level is the most effective way to produce the finish you want. Depending on the primer you are using it may take 4 or 5 coats of primer to cover up the wood. If you had the means of spraying Bushwacker white lacquer primer from Sherwin Williams works really well.
Years ago this would be handled by using a good sharp scraper but sandpaper seems to be the only alternative folks consider now. The raised portion of the grain is harder than the pulpier and softer wood between. If you scrape but don't push down real hard you may be able to erase any grain lines. Depends on the wood.
I'm certain some folks have mentioned the following book but I'll do it again. If you want to discover some older methods, with the focus NOT on sanding everything that moves, try finding this. He has a second book (The Furniture Doctor) but this one is the best reference I can find for dealing with wood finish hassles of any kind. It was written around mid-20th century but most can be applied today. I have the original print edition and already have three family members claiming them after my demise. I didn't really understand lacquer until finding these.
From Gunk to Glow: The Gentle Art of Refinishing Antiques and Other Furniture Paperback – January 1, 1983
by George Grotz
As far as the two species of wood, poplar would have less of a grain problem and paint better than the pine. Poplar has a very tight grain, more like soft maple where the pine does have some hard bands of grain. If you avoid water based paints either should paint fine. The water in water based paints will raise the grain taking more coats and sanding between coats to achieve the same results.
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