Which paint to use

I thought this question was better suited to finishing and hence posting it here and not in the paint section.
I am building a reading desk for the girls, and have been requested to do it in Pink, no surprises there.

I was wondering how to go about it and what paints to use.
The finish I am after is similar to the smooth finish you get on laundry cabinets (pics attached).
I know the final finish will either be a lacquer or polyurethane finish, but trying to understand what the substrate paint is.

The process that i was thinking of doing was.
1. sand to 120
2. apply oil.enamel undercoat
3. sand to 220
4. apply enamel paint
5. sand it down smooth
6 apply again
7 apply a PU top coat

This was going to be something like this from bunnings
https://www.bunnings.com.au/intergra...inish_p1520108

But I am not sure if this is correct and/or am I using the right type of paint and PU topcoat.
Any help or advice is most appreciated.

Thanks

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There's a option to sanding which you might consider.
Sandpapers shred the surface, coarse or fine, still shredding scratches.

Extremely coarse steel wool has flat strands, not round.
Gently rubbed over a surface, those flat strands cut like a thousand little chisels.
That effectively cuts off raised grain.
Next, you panit over it = smooth.

I do this quite a lot with wood carvings, dishes, that I expect to be handled.
But all the curved surfaces are really difficult to sand smoothly.
A few wipes with coarse steel wool = done.

I think you'll need to use 2 or 3 coats of colour and maybe 4 or 5 coats of poly so that after sanding you still have enough finish on the desk.

Thanks, for your help, just went and got a primer from bunnings and working on a sample piece right now.
plan has changed from enamel based to acrylic based, hoping i will be able to apply a polly coat on it.
LOoks like it is going to be as Ian suggested, few extra coats of poly and then sand and polish with a cutting compound.
Only need it to be reasonable, not looking at absolute brilliant finish as the kids will take all of 1 hour before there are cut and scratch marks in it.
Thanks
Harender