If you are buying one (1) overcoat, then you would regret buying a full length trench coat with zip out liner.
No other overcoat is as versatile. Single breasted is probably easier to dress up and down, but ymmv.
Since, you live in the city, you really need both a trench coat and an overcoat.
In fact, you really need three overcoats, if you can find a thrifted pea coat/car coat style along the way, unless you already have some sort of casual overcoat like a parka or leather jacket.. A shorter length coat has its advantages depending on how you live, but it will never replace a full length coat for warmth when it is near or below zero weather, especially when the wind is brisk.
If your budget is tight, get one of either your overcoat or trench from a thrift or consignment store.
Since you are usually business casual, I would make your thrift buy the Chesterfield, unless you stumble into a particularly fortunate find on a thrifted Burberry trench coat first. Keep an eye out for a tweed overcoat that you find attractive. I have one with a very subtle charcoal plaid tweed with brown undertones and subdued red overcheck that can serve for anything below black tie rig, and not that anyone would bat an eye, if I wore it to a semi-formal occasion nowadays. I just prefer other options.
So all things being equal, find your trench coat first, since it will be harder to find a great value that will last and fit well.
You can dress a charcoal herringbone Chesterfield up or down pretty easy, as well as a polo coat in natural camel hair, which is considered is more casual than the Chesterfield. The polo might be good if you dig the idea of camel hair as it is very warm for it's weight But if you can't store it properly, moth larva will make you regret its purchase of any camel hair garment or cashmere for that matter.
The dressiest option for you would be a full length blue cashmere overcoat. Awesome and warm, but there is no real good way to dress it down without looking like a gangster from 1930's.But, if you are headed to Lincoln Center, the Met, or an important business meeting, nothing will make you look as classy as navy or midnight cashmere.
A dark horse for you might be a covert coat for spring and fall wear if you can find a real one, and not one designed to be fashion statement. You would wear it, instead of the trench coat sans liner on days when you're not likely to get wet and it's above freezing, but you want more coverage than a car coat, pea coat, parka, or bomber.
I passed on the idea of a herringbone Chesterfield and went straight to blue cashmere for my dress overcoat, since I already have winter overcoats in of plaid tweed and camel hair. that are each awesome with anything from lounge suits to black jeans. When I wear my plaid tweed with a black watch cap and black jeans, I can even pass for a homeless guy when required, lol!
But all my overcoats stay home when the weather is snotty or wet, as I prefer to wear a trench coat for such an occasion.
Good luck with your adventure in finding a warm overcoat that you'll enjoy for at least the next 30 years.