The creature types are Fey, Celestial and Fiend
For a simple summoning, Sprites are fey, while Quasits and Imps are fiends. That leaves the question open for the pseudodragon. It can be a fey, celestial, or fiend in the form of a pseudodragon (as the spell description states). Nothing in the pact description contradicts that.
When you cast the spell, you can choose one of the normal forms for your familiar, or one of the following special forms.
Without getting complicated, three out of four special forms already coincide with fey, fiend, or celestial. The pseudodragon (form) can be any of the three, since the spell's features otherwise hold in this case. (PHB p. 107).
The form and the spirit don't have to match if the Warlock wants to mix it up.
That could be fun.
Mix and match? Sure, nothing prohibits it
You gain the service of a familiar, a spirit that takes an animal form
The familiar is a spirit that takes a form. That's as specific as the spell gets, beyond it having to be a beast (for a regular casting of find familiar - beasts from the list), or the additional choice of special creatures if it's a summoning from a Warlock with Pack of the Chain. (The Warlock could summon a weasel form if they wanted to; they don't have to summon a special).
If the Warlock so desires, they can summoning a fiend spirit in the form of a sprite or a celestial spirit in the form of an imp. All that changes is the form; that's a special feature of the Chain Pact. Whether or not that makes sense is up to the Warlock in question.