For the purpose of the question, I will use a very well known spell as the basis, magic missile, which is a 1st level spell.
Casting a quickened spell is a swift action. You can perform another action, even casting another spell, in the same round as you cast a quickened spell. A spell whose casting time is more than 1 round or 1 full-round action cannot be quickened.
A quickened spell uses up a spell slot four levels higher than the spell's actual level. Casting a quickened spell doesn't provoke an attack of opportunity.
A heightened spell has a higher spell level than normal (up to a maximum of 9th level). Unlike other metamagic feats, Heighten Spell actually increases the effective level of the spell that it modifies. All effects dependent on spell level (such as saving throw DCs and ability to penetrate a lesser globe of invulnerability) are calculated according to the heightened level. The heightened spell is as difficult to prepare and cast as a spell of its effective level.
Now lets take that spell and apply quicken spell. The new quickened magic missile requires a 5th level spell slot to cast, but the DC is still a first level spell and for purposes of Spell immunity or lesser globe of invulnerability its also a first level spell.
Now if you were to apply heighten spell. I choose my quickened magic missile. Am I allowed to create it as a 5th level spell and thus not use a higher slot or must it be higher, or is it forced to be higher?