In 5e RAW: Spell save DC is 8 + proficiency bonus + spellcasting modifier (WIS modifier, for clerics)
It is not affected by the level of the spell or spell slot used.
The save that the target rolls depends on the spell. Hold Person has them make a WIS save, for example. This means that the target rolls a d20, adds their WIS modifier and, if they have proficiency in WIS saves, adds their proficiency bonus. If it's equal to or higher than the caster's spell save DC, they pass the save (which might mean they shrug off the effects or take half damage or something; it depends on the spell)