You already got good advice what to do for the issue.
First, if you are a true amateur, you need to consider woodworking as a hobby! You sanding job from the pics posted is top notch and VERY impressive! I will say this- you did such an awesome job sanding that desk, it would have been beautiful stained! Almost a mortal sin to paint it! Plus you didn't have to go that far sanding if you were just painting it.
Second, as an amateur here is a little "why" versus "what." They gave you a latex primer, which is water based. The second it hits the surface, it can raise grain. It also will always let the surface remain porous and, thus, will allow some moisture movement inward and outward from the wood. That means you don't want to cover it with something like the oil paint you have, as it will result in trapped moisture which means paint that will eventually (may take decades in some cases) fail in some way. When doing furniture, oil primer always gets oil paint and latex primer gets latex paint
But when you are going to paint wood, you can get bleed through. Different grains and the summer bands in the wood will create blotching. All that fine sanding you did opened those pores up to sucking your primer in. When painting wood, you need to close those pores up and seal them so moisture won't escape and your paint will adhere to a level, sealed surface. For that you need a "sealer." The sealer coat envelopes the porous wood, preventing the first few coats of lacquer from being excessively absorbed. Kilz or Zinsser or BIN. Keep in mind sealer is not paint. Its a sealer. Do one coat.
Now you have to decide about the grain. You will likely still see the grain from an angle. It won't be a bleed through when painted, but you will see the pattern. Do you want to keep that of not? If you are OK with that, skip this step. If not, you need use a wood filler. Wood filler is a paste like paint. You use a flat blade to apply filler in two very thin coats, one following the grain of the wood and the other crossing the grain. Let the first coat dry thoroughly, for at least several hours, then sand it with fine-grit paper. It will level the surface out so you will never see the grain pattern.
Now you put another coat of sealer on. Once dry, you are ready to paint!
As for oil paint- its more durable than latex. The downside is any wood furniture painted with oil paint will yellow over time. There is no way around it. It will vary depending on the original color and how much sun it gets. White oil based paint will have the most noticeable yellowing. It may take 5 years, it may take ten, it will yellow. Any finisher who tells you different is a flat out liar. There is no way to avoid it! Additionally, if applied too thick or too fast between coats, it will peel and crack in addition to yellowing. The paint you have in the red cans from SW is EXCELLENT- BUT WHY DO YOU HAVE TWO DIFFERENT WHITE COLORS? Those are two different base colors, one white and one tinting white! If you are painting it all one color, those cans should be identical! Fix that before you paint! You can mix the two in a spate container or just go exchange one so they match.
Two coats with plenty of drying time between! Don't let anyone, including the label on the can tell you to put more than one coat on every 12 hours!
Post pics when you are done!
A very basic guide to finishing wood furniture is below for your future projects:
Painting Bare Wood:
-Water/TSP wash
-Sealer
-Wood fill (if doing)
-Sealer again if you used wood fill
-Primer (latex or oil)
-Paint 1 (same type as primer)
-Paint 2
Staining Bare Wood
-Tack cloth wiping
-Apply coat of pre-stain conditioner
-Stain coat 1
-Stain coat 2
-Poly 1
-Sand
-Poly 2
-Sand
-Poly 3