Dull question alert - primer vs ordinary emulsion

[Professionalworrier]

I've been having a debate with my DH re:using specific primer paint on our new house build walls.
I want to use a primer on our walls before painting. I figure we only get one chance to paint the walls for the first time and want to use the best product.
My DH on the other hand thinks we should just get any cheap emulsion. He suggested one that cost 10 pounds for over 10L. The one I have in mind isnt expensive but definitely not that cheap
So am I a marketing persons dream and my DH is right, anything will do and cheap is just as good? Or am I right and we will notice using cheaper products in the long run?
Anybody have any experience in this area? TIA

its had a mist coat already i assume?

@GirlCrush no, no mist coat just freshly plastered walls and that have dried out now. Excuse my ignorance but what is a mist coat?

For brand new plaster, I'd dilute emulsion and apply that (mist coat above).
Then straight to 2 coats of whatever colour you want.
No primer needed for new plaster.

@TierFourTears ah ok. I didnt realise it was called a mist coat. I was calling it an undercoat. The primer is designed for new walls. However I'm a sucker for a good marketing sell so I have myself convinced I need it

You only need to mist coat if your plaster has just appeared to be dry. If it’s been dry a while go straight in with emulsion if you’re going dark you can use a mid grey priming coat so you may only need one coat on top

@Amyheadache thank you we are going for a deep navy in one room so I'll try that.