For the vast majority of jobs, eggshell is what you want on woodwork and trim. It's the sweet spot: tough enough to take a wipe and the odd hoover knock, low-sheen enough to look contemporary rather than dated. Full gloss has fallen out of fashion in homes — it flags every dent and brush mark, and it shouts "1985". Satin sits between the two and is a fair middle ground if you want a touch more durability without going full shine.
For a quality water-based eggshell that brushes beautifully and yellows far less than old oil-based finishes, Little Greene Intelligent Eggshell and Farrow & Ball Modern Eggshell are both cracking. Dulux Heritage Eggshell is another solid choice with a slightly flatter sheen. If you're after a properly hard-wearing, self-levelling finish on a high-traffic banister or front door, the old-school oil-based eggshells still have an edge on toughness — but the modern water-based ones have caught up enough that I'd only reach for oil on heavy-use joinery.
The usual "but what about" is colour matching. Trim is traditionally a shade off your walls rather than brilliant white — it softens the whole room. Farrow & Ball Pointing is the classic warm off-white for trim, and Slipper Satin works a treat against creamier walls. If you want trim to recede quietly, paint it the same colour as the walls in eggshell — that "colour drenching" look is bang on trend and makes a small room feel bigger.
Practical advice: prep is everything on woodwork. Sand back, fill any dings, and prime bare or stained wood with Zinsser BIN (knots, tannin, old varnish) before your topcoat. Two coats of eggshell, lightly de-nibbed between coats with fine paper, and you'll have a finish that wears for years. Don't skip the caulk where trim meets wall — it's the difference between a tidy job and a dodgy one.