Tiles want a hardwearing, wipeable finish, which means eggshell or satin — never matt. Matt has no abrasion resistance and will scuff and water-mark on a surface you're going to be wiping down constantly. Eggshell gives you a soft sheen that's easy to keep clean; satin a touch glossier and even tougher. Full gloss is also viable on tiles and the most scrubbable of the lot, but it shows every brush mark and any imperfection in the original tile surface, so most people land on eggshell as the sensible middle ground.
Now the bit that actually matters: the topcoat is the least important part of painting tiles. Tiles are glazed, non-porous and slick — nothing grips them without help. The whole job rests on the primer. Use a proper adhesion primer like Zinsser BIN (shellac-based, bites onto glazed surfaces beautifully) or Zinsser Cover Stain. Skip this and your lovely eggshell will peel off in sheets the first time it gets knocked or steamed.
For the topcoat itself, an oil-based or hybrid eggshell holds up best in wet areas. Little Greene Intelligent Eggshell is a strong, water-based, wipeable option, and Farrow & Ball Modern Eggshell works well on splashbacks and tiled walls away from constant standing water. For something soft and timeless on a kitchen splashback, Farrow & Ball Slipper Satin or Pointing reads clean without going stark, while Cornforth White gives a gentle warm-grey if you want a bit of depth.
The "but what about" — floor tiles and shower enclosures. Be honest with yourself here: heavy foot traffic and permanently wet zones are brutal on painted tile, and even a perfect primer-and-eggshell system will eventually wear through. Painting tiles is brilliant for splashbacks, fireplace surrounds and feature walls; it's a gamble in a shower tray or busy hallway floor.
Practical advice: degrease thoroughly with sugar soap, give the tiles a light key with fine abrasive, prime, then two coats of eggshell with proper drying time between. Don't get water near a painted splashback for a week while it cures hard.